Maths algebra
Use algebra to solve story puzzles If you double the age that I will be in 5 years time, you will get the my mothers age now. My mother is 38. How old am I?
Let my age=a In 5 years time I will be x+5 My mothers age is 38 2(x+5)=38 2x+10=38 2x=38-10 2x=28 X=14. I am 14 years old Tip; reread the question at the end and write it with correct units eg years old
Solve x/3 +5 = 2
x/3 +5 = 2 X/3 =2-5 X/3= -3 Then times both sides by 3 X= -9
Solve x/4 +3= 2x
x/4 +3= 2x. Tip: Get rid of the fraction first by multiplying ALL TERMS by 4 X+12= 8x 12=8x-7 (-x) Tip; collect x's on side with most x's 12=7x 12/7=x
Solve x²=4
x²=4 so x=±2
What is y⁸ ÷ y²
y⁶ (subtract the powers)
What is y³ x y⁵
y⁸ (add the powers)
What is (y²)⁴
y⁸ (multiply the powers)
What is √a x √b? e.g. √2 x √3
√ab √2 x √3 = √6
3x+4y=14 -2x+5y=6
2,2 3x+4y=14. (X2). 6x+8y=28 -2x+5y=6. (X3). -6x+15y=18 Tip: multiply the two equations to get the same number of x's or y's EG multiply top equation by 2 multiply bottom equation by by 3 then add them up to get rid of x 23y=46. Y=2 Then substitute into 3x+4y=14 3x+8=14 3x=6. X=2
What is 2a² when a is 3?
2a²= 2xaxa =2x3x3=18 Tip The ² stays ONLY with the term it is NEXT TO unless there are brackets ... in this case only a is squared
Substitute x=3 into x+2
3+2= 5 Substitution means replace the x with the number 3 in this case just as in a sports team substitution of players
What is(2a)² when a is 3?
(2a)²= (2a)x(2a)= 4a² = 4x3x3=36 Tip; As there are brackets it is the 2a term that squared this time
What is x⁰
1
Simplify 1. a²b+ a²b+ a²b+ a²b+a²b 2. a²b x a²b x a²b x a²b
1. 4a²b 2 a⁸b⁴ Tip: When multiplying add the indices OR write out all in full first and count them up e.g. aabxaabxaabxaab=a⁸b⁴
Simplify 1. a + a+ a + a + a 2. a x a x a x a x a
1. 5a 2. a⁵ Tip: check carefully if it is multiplication or addition
Solve 1/3 (2x+1)=5
1/3 (2x+1)=5. Tip: get rid of the fraction first by X ALL TERMS BY 3 2x+1=15 2x=15-1 (-1) 2x=14. (Divide by 2) X=7
What is 2x(x+6)-5(x-2)=
10x²+12x-5x+10 =10x²+7x+10 ALWAYS REMEMBER THE NEGATIVE BEFORE AND INSIDE A BRACKET CHANGES THE SIGN (-x-=+) this is a common trick look out for it ;(
What does factorise mean?
Putting the brackets back in.
Solve 2x+3=7
Rule is always do the same to both sides 2x+3=7 2x=7-3 (-3) 2x=4 (Divide by 2) X=2
Simplify 3xy² ÷6xy
Tip: write divisions in algebra as fractions then cancel Tip: write out indices in full to make cancellation easier 3xy² ÷6xy = 3xyy/6xy =y/2
Solve x+y=12 x-y=8
Tip; LOOK both have the same number of y's but one is + and one - So ADD the equations this time to eliminate y
Solve 2x+y=4 x+y=3
Tip; LOOK both have the same number of y's) SUBTRACT the equations to eliminate y
Solve 6w + 1 = 4w + 13
Tip; collect the w's on the side with the most w's to keep in +ve numbers
How do you solve simultaneous equations by substitution?
Turn one equation around so that x=...or y=.... then substitute that expression back into other equation and solve
What method do you use to expand 2 brackets? eg (x+3)(x-1)
Use FOIL
Solve X/3=2
X/3=2 (Times both sides by 3) X=6
What is (√a)²?
a e.g. (√3)² = √3 x √3 = √9 = 3
