English Practice Tests

Question 1

1.4 The vertices of a rectangle are (-1, -2), (4,-2), (4, 3), and (-1, 3). When the rectangle is graphed in the standard (x,y) coordinate plane below, what percent of the total area of the rectangle lies in quadrant III?
A. 12%
B. 8%
C. 32%
D. 6%
E. 12.5%

Answer 1

B.

1) find the length of each side using the vertices
2) multiply the sides to find the area
3) Find out how many units are in Quadrant III
4) Divide that by the number of total units
5) That gives the %

Question 2

1.23 If x and y are positive integers such that the greatest common factor of x^2y^2 and xy^3 is 45, then which of the following could y equal?
A. 45
B. 15
C. 9
D. 5
E. 5

Answer 2

D.

1) The greatest common factor is xy^2
2) set this = to 45
3) (5)(3)^2 = 45 OR (45)(1)^2 = 45
4) 1 is not an option provided so by default the answer is 3

Question 3

1.27 Graphed in the same standard (x,y) coordinate plane are a circle and a parabola. The circle has a radius of 3 and center (0,0). The parabola has vertex (-3, -2), has a vertical axis of symmetry, and passes through (-2, -1). The circle and parabola intersect at how many different points?
A. 0
B. 1
C. 2
D. 3
E. 4

Answer 3

C.

1) sketch it and see

Question 4

1.37 What is the length, in coordinate units, of the altitude from C to AB in Triangle A(1,1)B(7,1)C(2,4)?
A. 3
B. 5
C. 6
D. 10^1/2
E. 13^1/2

Answer 4

A.

1) find the distance of 7 between the highest point and the lowest point. This is point C and B

Question 5

1.40 License plates i=on cars in a certain state consist of 3 letters taken from the 26 letters, followed by 3 digits taken from the 10 digits, 0 - 9. What is the expression that gives the number of distinct license plates that are possible given that repetition of both letters and numbers are is allowed?

Answer 5

10^3 x 26^3

1) if there was a ! in the equation it would not allow repetition

Question 6

1.45 Change this standard form of an equation into slope form
2x - 5y = -5

Answer 6

y = 2/5x +1

Question 7

1.46 Diana is baking bread, and the original recipe calls for 1.5 teaspoons of yeast and 2.5 cups of flour. Diana will use the entire contents of a packet that contains 2.25 teaspoons of yeast and will use the same ratio of ingredients called for in the original recipe. How many cups of flour will Diana use?
A. 1 7/8
B. 3 1/4
C. 3 1/2
D. 3 3/4
E. 4

Answer 7

D.

1) 1.5x = 2.25; x = 1.5
2) 2.5(1.5) = 3.75

Question 8

1.56 Whenever j and k are positive integers such that (√3)^j = 27^k, what is the value of j/k?
A. 1/6
B. 3/2
C. 3
D. 4
E. 6

Answer 8

E.

1) use the properties of exponents
2) 3^j/2 = 3^3k
3) j/2 = 3k
4) divide by k, and multiply by 2
5) j/k = 6