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. 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. 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.

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. 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. 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. 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. 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. 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. 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.