EASA Part 66 : Mathematics Question2

Question Number. 1. In the following equation what is the y-intercept? 4y = 2x + 8. Option A. 2. Option B. 4. Option C. 8.

Correct Answer is. 2. Explanation. First get rid of the 4 from RHS (divide all by 4) y = 0.5x + 2. Intercept with y-axis is when x = 0. So put x = 0 and what is left? (remember that 0.5 x 0 = 0).

Question Number. 12. What is commonly referred to as the law of a straight line?. Option A. y = x2 plus 180. Option B. The line must pass through the 180 degree datum. Option C. y = mx + c.

Correct Answer is. y = mx + c.

Question Number. 15. What is the equation of a straight line with gradient m and intercept on the y axis c?. Option A. y = mx + c. Option B. x = y + mc. Option C. y = cx + m.

Correct Answer is. y = mx + c.

Question Number. 17. Two lines with equations y = 3x-6 and y = 3x + 4 ?. Option A. meet when y = 3. Option B. are at right angles. Option C. are parallel. Correct Answer is. are parallel.

Explanation. They both have the same gradient i.e. 3 and hence are parallel.

Question Number. 16. What is the gadient of the straight line whose equation is 2y + 3x = 6?. Option A. 3. Option B. 3/2. Option C. -3/2.

Correct Answer is. -3/2. Explanation. First put into the form y = mx + c, i.e. y = -3x/2 +3 m = gradient hence gradient is -3/2.

Question Number. 14. A straight line passes through the two points (1,4) and (6,1). What is the gradient of the line?. Option A. 3/5. Option B. -3/5. Option C. 2/5.

Correct Answer is. -3/5. Explanation. The gradient is found by dividing the difference between the y coordinates by the difference between the x coordinates. In this case it will be 4-1/1-6 = 3/-5 =-3/5.

Question Number. 2. How many times does the x-axis get crossed when y = x2 -3. Option A. 3. Option B. 1. Option C. 2.

Correct Answer is. 1. Explanation. y = x2 (a quadratic) is a shape like a 'U-curve' where the bottom of the 'U' sits on the (0,0) point. The -3 means the 'U' is shifted down the y-axis 3 places.

Question Number. 11. What is the slope between the points (3,1) and (9,3)?. Option A. 1/3. Option B. 3/1. Option C. 2.

Correct Answer is. 1/3. Explanation. (Y2-Y1)/(-), 3-1 = 2, 9-3 = 6. 2/6 = 1/3.

Question Number. 5. The graph points (9, 3) and (3, 1) what is the slope?. Option A. 9/5. Option B. 1/3. Option C. 3/1.

Correct Answer is. 1/3. Explanation. Slope = change in Y / change in = (3-1)/(9-3) = 2/6 = 1/3.

Question Number. 13. The y intercept of 4y = 4x + 8 is. Option A. 4. Option B. 8. Option C. 2.

Correct Answer is. 2. Explanation. Must be in form y = Mx + C, C is y-intercept. y = x + 2 in this case.

Question Number. 3. On a graph what is the intercept of y when 4y = x + 8. Option A. 4. Option B. 8. Option C. 2.

Correct Answer is. 2. Explanation. Use y = mx + c The 'c' is the y-intercept. 4y = x + 8 must be converted to y = 1/4x + 8/4".

Question Number. 6. A straight line graph has the equation 3y = 12x-3 What is the gradient?. Option A. 1/4. Option B. 4/1. Option C. 3/4.

Correct Answer is. 4/1. Explanation. The coefficient of x is the gradient, but only when the equation is in the form y = mx + c. So y = 12/3x -3/3 12/3 = 4/1.

Question Number. 10. 2y = 5x + 3 What is the gradient?. Option A. 2/5. Option B. 5/2 + 3. Option C. 5/2.

Correct Answer is. 5/2. Explanation. Gradient is the m when the formula is in the form y = mx + c.

Question Number. 7. For an equation 2y = 5x + 3 what is the gradient?. Option A. 3/5x. Option B. 5/2. Option C. 5x+3/2.

Correct Answer is. 5/2. Explanation. y = mx + c Gradient is the 'm' (but the coefficient of y must be 1. If it is not, divide all terms by the coefficient of y).

Question Number. 8. Using cosine to find the angle of a triangle, which statement is true?. Option A. Opposite/Hyp. Option B. Opposite/Adjacent. Option C. Adjacent/Hyp.

Correct Answer is. Adjacent/Hyp. Explanation. S.O.H.C.A.H.T.O.A.

Question Number. 24. Which of the graphs shown is given by the equation; 2y = 4x +6 ?.

Correct Answer is. B is correct because y = ax + b, is equation of straight line. Explanation. y = ax + b is a straight line, y = ax2 + b is a quadratic which has one turning point y = ax3 + bx + c has two turning points.

Question Number. 23. Which of the graphs shown is given by the equation y = x2 + 3?.

Correct Answer is. C is correct. Explanation. y = ax + b is a straight line, y = ax2 + b is a quadratic which has one turning point, y = ax3 + bx + c has two turning points.

Question Number. 25. Which of the graphs shown is given by the equation; y = 2x3 + 4x + 3 ?.

Correct Answer is. Graph in C is correct, because it has two turning points. Explanation. y = ax + b is a straight line, y = ax2 + b is a quadratic which has one turning point, y = ax3 + bx + c has two turning points.

Question Number. 9. What type of equation is y = x2 + 9x + 14?. Option A. Quadratic. Option B. Circular. Option C. Exponential.

Correct Answer is. Quadratic. Explanation. Quadratic has x2 as its highest order.

Question Number. 22. The plot of the equation y = 1/x is a. Option A. straight line. Option B. curve with one turning point. Option C. curve with two turning points.

Correct Answer is. curve with two turning points. Explanation. y = 1/x is a curve with two turning point. Try plotting it with values of x of -2, -1, 0, 1, 2 and you will see that it appears in the no.1 and no.3 quadrants and goes off to infinity.

Question Number. 19. The line with equation x = 3 is. Option A. at 45° to both axes. Option B. parallel to the x axis. Option C. parallel to the y axis.

Correct Answer is. parallel to the y axis. Explanation. If x = 3 then the line will pass through all points where x=3 i.e. (3,0); (3,1);(3,2) that is a line parallel to the y axis.

Question Number. 21. Use the graphs to solve the simultaneous equations y = x + 2 and 3y + 2x = 6. Option A. x = 2, y = 0. Option B. x = 0, y = 2. Option C. x = 0, y = 0.

Correct Answer is. x = 0, y = 2. Explanation. This is easy. The solution is the point when the lines cross, i.e. (0,2): x=0, y=2.

Question Number. 4. What is the equation of the line shown?. Option A. y = 2x + 2. Option B. y = -2-x. Option C. y = x-2.

Correct Answer is. y = -2-x. Explanation. Slope (gradient) is 2/2 and is negative (i.e. -1). y-intercept is -2. Equation of the line (y = mx + c) is y = -1x -2 or y = -2-x.

Question Number. 20. What is the equation of the graph shown?. Option A. y = -2. Option B. x = -2. Option C. y = 2x.

Correct Answer is. y = -2. Explanation. All the points on he line have a y value of -2, hence the equation is y = -2.

Question Number. 18. What is the equation of a straight line that passes through the two points (0,0) and (3,2). Option A. y = 3x + 2. Option B. y = 2x + 3. Option C. y =2x/3.

Correct Answer is. y =2x/3. Explanation. Gradient of the line is (2-0)/(3-0) = 2/3 this is the difference in the y values divided by the difference in the x values; m =2/3, The intercept on the y axis is 0, that is when x = 0 ; c = 0, The gradient of a straight line is of the form y = mx + c so we get y = 2x/3 +0 = 2x/3.