Mathematics exam questions 10F

In August 20% of Ria's gross earnings was deducted as tax. How much money does she have left after the deduction?

$1971.00 20/100 x 2463.75 = 492.75 2463.75 - 492.75 = $1971.00

Irish Potato costs $250 per pound. 12 pound was purchased and a discount of 21% was given. How much money was spent? ​

$2,370 12 x 250 = 3000 21/100 x 3,000 = $630 3000-630 = 2,370

Ria invested $219 of her earnings for 3 years at a rate of 4.5% per annum simple interest. How much interest doe she receive after 3 years? I = PRI/100

$29.57 I = 219 x 4.5 x 3/100 = 2,956.50/100 = $29.57

$5000 inclusive of 10% tax was used to purchase a device, what was the original cost of the device? ​

$4,545.50 5000 inclusive of 10% tax = 5000 = 110% since 5000 is already 100% but 10% is added so put 100/110 x 5000 = 4,545.50 remember this is wrong Because the $ sign isn't there $4,545.50 now it's right.

Ria is paid at the rate of $13.50 per hour. During a certain week she worked 40 hours. How much did she earn that week?

$540.00 $13.50 = 1 hour $13.50 x 40h = $540.00

6nx - 9mx - 4ny + 6my

(2n-3m) (3x -2y) 3x (2n - 3m) -2y (2n-3m) (2n-3m) (3x-2y)

Factorize completely 4x²-9 ​

(2x-3) (2x+3) Foil to turn back 4x²-6x + 6x -9 4x² - 0 -9 4x²-9

Factorize 2x² - 6x +4

(2x-4) (x-1) 2x 4 = 8 2x²- 2x - 4x + 4 2x (x-1) -4 (x-1) (2x-4) (x-1)

2x² + 3y + y²

(x+y) (2x+y) 1. 2x² + 2xy + xy + y² 2. 2x (x+y) + y(x+y) (x+y) (2x+y)

Chance of taking 3 oranges out of a box, when there are 2 apples as well Chance of taking 1 orange

1. 3/5 2. 1/5 All items = denominator What you'll get = numerator. Use 1/2 of heads or tales as a basis. Or the chance of getting everything is low so it's the denominator.

The stadium in Qatar that host the fifa world cup finals can seat 50,000 persons. If for the first 15 mins of the match the stadium was at 81% capacity, how much seats were filled? After renovation they were up to 60,000 seats, what was the percentage increase?

1. 40,500 81/100 x 50,000 = 40,500 seats 2. 60,000 - 50,000 = 10,000 Difference of raised amount and original number of seats ÷ original number x 100 = percentage increase 10,000/50,000 x 100 = 20%

In a bus of 60 students. 75% of the students are males. How many are males If 20% of the females are in grade 10, how many girls are in grade 10?

1. 75/100 x 60 = 45 Females 60-45 = 15 males 25% x 60 = 15 males 2. 20/100 x 45 = 9 girls

2^-3 -8 -1/8 1/8 8

1/8 2^-3 in calculator = 0.125 0.125 into a fraction = 125/1000 reduced = 1/8

Emma says the length of her favourite movie is 129 minutes, but she has rounded the time to two significant figures. Which could be the number of minutes of Emma's favourite movie before she rounded it? 111.25 115.95 124.9 133.2

115.85 Round 115.85 to 2 sig fig is 120.00 to 120 (should be 12?) No because you have to list number before decimal

what percentage of 340 is 425?

125% 425/340 reduced = 125/100 after 125/100 x 340 = 425 to verify

A plot of land I'd values at $18 000. Land tax is charged at the rate of %0.70 per $100. What is the total amount of tax to be paid for the land? a. 110.00 b 126.00 180.70 257.15

126.00 18000/100 = 180 land 0.70 x 180 = 126.00

The ratio of food to juice is 3:5. Infact there are 30 more juices than food. How much food was prepared?

15 Fine difference of two ratios. In this case it's 2. 30÷2 = 15 30/2 = 15 so 1 share = 15 2 share = 30 I did it another way by doing 3-5 x-25 75 =5x x=15 but may be wrong, but you can do it to verify

If 60% of a number is 90, what is the number? 30 54 150 180

150. 60/100 x 150 =90

Ria worked 4 weeks in the month of August and her gross earnings were $2,463.75, Her regular week comprised 40 hours and overtime was paid at 1 1/2 times the hourly rate. Show that Ria worked 15 hours overtime in August. Her hourly rate is $13.50

15hours $2463.75 = Both regular pay and overtime 13.50 x 40 = $540.00 540 x 4 = $2160 $2463.75 - 2160.00 = 303.75 3/2 x 13.50 = 20.25 = hourly rate 20.25 ÷ 303.75 = 15

The value of the digit 2 in 425.3 is 2 tenths 2 ones 2 tens 2 hundreds

2 tens. Start from before the decimal, three would be tens and 2 would also be tens, 4 would be hundreds

What is 4 1/3 - 1 5/9 (/1 3/7 x 1 2/3

21/20

The number 3.14063 written to 3 decimal places is. 3.140 b 3.141 c 3.146 d. 3.150

3.141 Places AFTER decimal

What is the number 32747 written to 4 significant figures? 32740 32750 3274 3275

3274 Just take the first four non 0 digits

What is the least number of plums that can be shared equally among 6, 9 or 12 children? 27 36 54 72

36 6, 9 and 12 are all factors of 36

18.96 x 2.03 correct to two significant figures is 0.38 38 38.19 380

38

What is the number 3754 expressed to the nearest hundred? 3700 3750 3800 4000

3800 Count from left to right, see if 754 is closer to 800 or 700. 749 = 700, 750 and up = 800

A carpenter purchases a piece of wood of length 40.8 centímetros long. He then saved 0.9 centímetros off both ends. What is the length of the piece of wood now? 39 centímetros 39.9 centimeters 41.7 centimeters 42.6 centimeters

39 centímetros 0.9+0.9 = 1.8 40.8-1.8 = 39

Find x+ 1/2 + x-2/4

3x/4

The four multiples of 4 are..

4, 8, 12, 16

Express 4 3/8 as a decimal correct to 3 significant figures. 4.30 4.37 4.38 4.40

4.38 Convert 4 3/8 into a fraction. After convert to a decimal by dividing. Next correct 4.375 to 3 significant figures. Take the first non 0 digits and round up by third digit (or last digit of the ordered amount of significant figure, and round it up) So 4.375 The 3 sig fig figures are 4.375, 7 is the last number, take the next number making it 75, round that part up to get 4.380 But only take 3 sig figs making it 4.38

The sum of 1/2 and 1/3 is a) 2/5 b) 3/5 c 5/6 d. 7/6

5/6 Find lcm of 2 and 3, multiply that by numerator, multiply denominators LCF = 6 1 x 3 = 3, 1 x 2 =2 2 x 3 = 6 3 + 2/6 = 5/6 (Butterfly method doesn't always work but you can use it to verify)

What is the midpoint of 55 and 60?

55 55+60/2 = 55

What Is x+2/3 + x-1/2?

5x + 1/6 Find lcm and multiply by numerator, the denominator will be the lcm In this case the lcm is 6 2(x+2) + 3(x-1)/6 6 is the denominator, after group 2x+4+3x-3/6 Group like terms 2x + 3x + 4-3/6 5x + 1/6 is the answers Rules= the lcm is the denominator don't multiply both denominators to make denominator, the denominator is just the lcm of both numbers

A property is sold for one and a quarter million dollars The two owners receive half the money each. How much do they each receive? 750,000 625,000 525,000 500,250

625,000 1,250,000/2

Expand and simplify (2x + 5) (3x - 4)

6x² + 7x - 20

Simplify 3(5x+2) -2(4x+3)

7x

In a classroom that facilitates 30 students, 80% of the seats are filled. How many seats are empty?

80/100 x 30 = 24 seats filled 20/100 x 30 = 6 seats empty or 30-24 = 6 seats filled

Children go to a Rodeo camp during the Easter holiday. Ms. Rekha buys bananas and oranges for the children at the camp. Bananas cost $3.85 per kg. Ms Rekha buys 25kg of bananas and receives a discount of 12%. How much money does she spend on bananas?

84.70 WRONG It's $84.70 3.85 = 1kg Banana. $3.85 x 25 = 96.25 12% Discount = 12/100 x 96.55 = 11.55 96.25 - 11.55 = $84.70

5 2/5 + 4 3/7 9 5/35 9 6/39 12/35 9 29/35

9 29/35

H.kayla invested a sum of money is a bank at compound interest rate of 5% per annum after 4 years the interest accumulated was $10,000. How much money was invested?

A = P ( 1 + r/100)^n Make P the subject P = A (1+r/100) P = 10,000 ( 1+ 5/100) ^4 P = 12,155.06 this is wrong the answer should be P = $12,155.06 This is correct.

The exact value of 37.26 divided by 1.8/1000 a) 0.207 b. 0.0207 c) 20.7000 d) 20,7000

B. 0.0207 Divide 37.26 by 1.8. Put that number over 1000 Divide the answer by 1000

Which of the ofllowing expressions does not have the same value as 49 x 20 Calculate what 49 x 20 and see which calculation = that sum a) 40 + 20 x 9 + 20 49 x 17 + 3 x 49 50 x 20 - 1 x 20 40 x 20 + 9 x 20

B. 49 x 17 + 3 x 4( (Remember to do pemdas because your operation can still be wrong)

There are 2 black socks. 3 white socks, and 4 brown socks. What is the probability that a white sock is NOT selected? The blue sock being selected And the Brown sock being selected Possibility of picking a white sock

Blue sock = 0/9 Possibility of picking a white sock =3/9 Possibility of not picking a white sock = 3/9 - 1/1 = 2/3 Picking a brown sock = 4/9 (Do simplify if possible)

29.94 x 0.5 is approximately a 0.15 1.5 15 150

C 15 14.97 when rounded up is 15 and is laso closest to 15 than the other answers

How much does a customer pay for an article marked at $50 if a sales tax of 6% is charged? $44.00 b $47.99 c. $53.00 d. $56.00

C. $53.00 6/100 x 50 = 3 50 + 3 = 53 C. = 53

The largest prime number that is less than 100 is: a 91 b 93 c 97 d 99

C. 97

The ciity government charges 5% property tax on the annual rental value of any property. What is the tax payable on a property which has a rental value of $135 per month> $27 b. $81 c. $128 d. $141

D. $141 5/100 x 135 = 6.75 6.75 + 135 = 141.75

Probability line

Impossible Even Likely Certain

The expression x² -6x + 7 can be written in the form (x+a)² + b, where a and b are constants. Determine the values of a and b and hence find the minimum value of the expression.

Minimum value = -2 x² -6x + 7 x²-6x (+9-9) + 7 (x-3)² -9 + 7=-2 a = -3 b = -2 You can start out with? I think? (-6/2 = -3) (-3)²=9

A student has $8.00 to spend on stationery. She buys two pens each costing $1.29 and a pack of paper costing $4.50. Does she have enough money left to buy a folder costing $1.40? yes - she has 2m21 left yes- she has $1.92 left No- she has overspend by $2.29 No- She only has $ 0.92

No- she only has $0.92 left ​

A bag contains 2 red cards, 4 green pens, 6 yellow oens and 5 white pens. What is the probability of choosing. One White Ball A white pen One yellow pen A yellow pen

One white pen = 1/17 A white pen = 5/17 One yellow pen = 1/17 A yellow pen = 6/17

Make V the subject of the formula. W = 5 + V/V-3

V = 5+3W/W-1 v-3W = 5+v VW - 3W = 5+V VW - V = 5 +3W VW - 1 = 5 + 3W V = 5 + 3W/W-1

What's theoretical probability

What's expected to happen.

The highest common factor of 18, 24 and 36 is a) 6 b) 18 c 36 d) 72

a) 6

There are 40 students in a class Girls make up 60% of the class. 25% if the girls wear glasses. How many girls in the class wear glasses? a 6 b 8 c 10 d 15

a) 6 60/200 x 40 = 24 girls 25/100 x 24 = 6 girls that wear glasses

Since 235 x 48.7 = 11 444.5, then 23.5 x 0.487 = 11.4445 114.445 c. 1,144.45 D. 11,444.5

a. 11.4445

On a math test, 20 students got 70%, 5 students got 90%, 1 student got 100% and 23 students got 50%. What is the probability that at random a student selected got A.50% B.70% C.90%. D. Not receiving 100%

a. 23/29 b. 10/3 c. 5/39 d. 38/39 Probability a student gets 100 percent is 1/39 A student not receiving 100 is 38/39. The number of students is the numerator for the grade they received The denominator 39 is from all the students ​

A shoe shop takes delivery of: Five pairs of shoes 2 pairs of books one pairs of slippers Calculate the probability of a box containing: a. shoes b. slippers c. Boots

a. 5/8 b. 1/8 c. 2/8 Numerator = outcome you'll get/all items/outcomes possibility of flipping a coin and getting heads = 1/2 use this as a basis

What number when added to 1 1/3 gives 2? 1/3 2/3 1 2/3 3 1/3

b) 2/3 4/3 + 2/3 = 6/3 reduce = 2/1 = 2 when denominators are the same, you just carry them to the next fraction ​

The next term in the sequence 1, 6, 13, 22, 33 is a)44 b) 46 c) 45 d) 52

b)46 A number by 2 is added to the previous number each time. first it's 5 added to 1. Making a sum 6. Then 7 is added to 6 to make 13. Then 9 is added to 13 to make 22 Then 11 is added to 22 to make 33 Then 13 is added to 33 to make 46 So we know the next term of sequence is 46

Express 0.12 as a fraction 1/9 3/25 1/8 3/5

b. 3/25

A custtomer saved $84 when he received a 30% discount off the regular price of a bag. What was the regular price of the bag? a. $196 b.220 c. 280 d. 364

c $280 30/100 x 280 = 84 This is how we know it's 280 Just place value in 30/100 x ( ) = 84

During a sale a shop allows 20% discount off the marked price of clothing. What will a customer pay for a dress eith a marked price of $30? a) $10 b) $20 c) $24 d) $30

c) $24 20/100 x 30 =6 30-6 = 24

Tom bought a pen for $60 and sold it to make a gain of 20% on his cost price. How much money did he gain? a) $12 b) $40 c) $72 d) $80

c) $72

Mr. Lee's salary is increased from $1500 to $2000. The initial salary expressed as a fraction of the new salary is a) 1/4 b 1/3 c 3/4 d 4/3

c) 3/4

(-1/2)^3 is the same as a -1/8 b. -1/6 c. 1/8 d. 1/6

c. -1/8 neg x neg = pos pos x pos = pos.

(-3) ^2 + (-2) ^2 a -13 b -10 c 13 d 25

c. 13

What percentage of 30 is 6? 5% 18% 20% 150%

c. 20% What % x 30 = 6 20/100 x 30 = 6

The exact value of 6 divided by 0.0003 is a) 200 b) 2000 c 20,000 d 200 000

c. 20,000

3076 in standard form 3.076 x 10-3 3.076 x 10^2 3.076 x 10^3 3.076 x 10^-2

c. 3.076 x 10^3

The number 0.0325 in standard form is a) 3.25 x 10-4 b) 3.24 x 10-3 c) 3.25 x 10-2 d) 3.25 x 10-1

c. 3.25 x 10-2

The 3xact value of 2 ÷ (0.01)² 0.0002 0.0005 5000 20, 000

d 20,009 used calculator

A man leaves home at 22:15 hours and reaches his destination at 04:00 hours on the following day in the same time zone. How many hours did the journey take? a) 5 b) 5 3/4 c) 6 d 6 1/4

d) 6 1/4

What is 125 x 9 expressed in scientific notation? 112.5 x 10¹ 11.25 x 10‐² 1.125 x 10-³ 1.125 x 10³

d. 1.125x 10³

mp + mq +np - nq

m (p+q) n (p-q₩

Factorize 3n^2 + 15np

n (3n + 15p)

How to find the probability of an event not occurring be less than '1'

not occurring = less from 1

p³-p

p (p-1) (p+1)

what is x/4 = 3

x = 12 X = 3 x 4 X=12

3 (x-2) = 6/5

x=2.4