QUESTION 1. In a given amount of time, James drove twice as far as Rachel. Altog

Question

QUESTION 1. In a given amount of time, James drove twice as far as Rachel. Altogether they drove 120 miles. Find the number of miles driven by each. Rachel drove ___ miles and James drove ___ miles.

QUESTION 2. Solve the following by extracting the square roots: X^2-4=0

QUESTION 3: Factor the Trinomial: x2 + 14x + 45

QUESTION 4. When should you use the quadratic formula?

ANSWERS:

When a quadratic equation CANNOT be factored easily or at all

When a quadratic equation CAN be factored easily

When a linear equation CANNOT be factored easily or at all

When a linear equation CAN be factored easily

QUESTION 5. Which of the following represents the general formula of a circle?

ANSWERS:

y = ax2 + bx +c

x2 + y2 = r2

Ax + By = C

y = mx + b

QUESTION 6. Determine whether the value of x=0 is a solution of the equation. 5x-3 = 3x+5

ANSWERS:

True

False

QUESTION 7. Which of the following would NOT represent a parabola in real life?

ANSWERS:

The McDonald’s arches

The trajectory of a ball thrown up in the air

The cables on a suspension bridge

A pitched roof

QUESTION 8. Mike works for $12 an hour. A total of 15% of his salary is deducted for taxes and insurance. He is trying to save $700 for a new bicycle. Write an equation to help determine how many hours he must work to take home $700 if he saves all of her earnings?

ANSWERS:

12h - .15 = 700

12h + .15(12h) = 700

h - .15(12h) = 700

12h - .15(12h) = 700

QUESTION 9. Determine whether the lines are parallel, perpendicular, both, or neither. L1: Y = 3X + 5 L2: Y = -1/3x + 5

ANSWERS:

Parallel

Perpendicular

Both

Neither

QUESTION 10. Find the slope of a line that passes through the given points (-2,1) (3,4)

ANSWERS:

3/5

5/3

-7/5

1/2

QUESTION 11. Graphically estimate the x- and y- intercepts of the graph: y = x3 - 9x

QUESTION 12. Plot the points and find the slope of the line passing through the pair of points (0,6), (4,0). Identify the correct graph from the ones listed below: 1st, 2nd, 3rd, or 4th.

QUESTION 13. If 3 is subtracted from twice a number, the result is 8 less than the number. Write an equation to solve this problem.

QUESTION 14. The expression 9/5 C+32 where C stands for temperature in degrees Celsius, is used to convert Celsius to Fahrenheit. If the temperature is 45 degrees Celsius, find the temperature in degrees Fahrenheit.

QUESTION 15. Evaluate the function q (x) = 1/(x2squared - 5) at q(3)

ANSWERS: 1/8 1/6 1/4 1/7 1/5 QUESTION 16. Multiply or find the special product: (x+4)(x+9)

QUESTION 17. Perform the operation and write the result in standard form: (3x2 + 5) – (x2 – 4x + 5)

QUESTION 18. Determine the x-intercept(s) of the quadratic function: ƒ(x) = x2 + 4x – 32

QUESTION 19. Select the graph of the quadratic function ƒ(x) = x2 + 3. Identify the vertex and axis of symmetry. Identify which of the graphs listed below is the correct one: 1st, 2nd, 3rd, 4th, or 5th.

QUESTION 20. Select the graph of the quadratic function ƒ(x) = 4 – x2. Identify the vertex and axis of symmetry. Identify the correct graph by noting it in the space below: 1st, 2nd, 3rd, 4th, or 5th.

Explanation / Answer

Q 1. Time taken by Rachel= Time taken by James

Let Distance covered by Rachel = x miles then distance covered by James = 2xmiles

In total the distance covered by both=( x+2x )miles= 120 miles

Thus x= 120/3 miles= 40 miles , thus Rachel drove = 40 miles and James drove = 2x= 80 miles.

Q2. x2-4=0

(x-2)(x+2)= 0 ; x= 2, -2

Q3. x2+14x+45= x2+9x+5x+45

=x (x+9)+5 (x+9) = (x+5)(x+9)

Q4. A quadratic formula is only to be used when a quadratic equation can't be factorised easily or at all.

Q5. The formula that represents the equation of a circle is

x2+y2=r2 , where x, y are the coordinates and r is the radius of the circle. The other equations , y= ax2+bx+c is the equation of a parabola. Ax+By= c , y=mx+c are the equations of a line.

Q6. To check of x=0 satisfy the equation, substitute x=0 in it and then the equation should be equal to 0.

5x-3=3x+5

5x-3x-3-5= 0 put x=0

0-0-3-5 = -8 hence x=0 doesn't satisfy the equation thus the answer is false.

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