SHSAT MATH PRACTICE TEST WITH ANSWERS

(1)  Five apples and 6 bananas together cost as much as 8 bananas and 9 pears.  One apple costs as much as 2 pears.  For the same price as 1 pear, how many bananas could be bought?

(A)  1  (B)  2  (C)  3  (D)  4  (E)  6

Solution

(2)  Let R = 8 · 9 · 7 · 13 and S = 4 · 6 · 11 · 49.  The greatest common factor of R and S is

(A)  12  (B)  42  (C)  56  (D)  168  (E)  504

Solution

(3)  What is the value of 4|x – y| - 3|xy| if x = -5 and y = 2?

(A)  -42  (B)  -18  (C)  -2  (D)  42  (E)  58

Solution

(4)  In the following sequence of eight numbers, each number has one more “1” than the number before it:

2, 12, 112, 1112,. . . . , 11111112

What is the hundreds digit in the sum of all eight of these numbers?

(A)  0  (B)  6  (C)  7  (D)  8  (E)  9

Solution

(5)  In Ms. Hsiao’s class there are twice as many boys as there are girls.  Half of the boys are in the math club and all of the girls are in the math club.  What percent of Ms. Hsiao’s class is in the math club?

(A)  25%  (B)  33  (1/3)%  (C)  50%

(D)  66 (2/3)%  (E)  75%

Solution

(6) The total cost to rent an inflatable slide for a birthday party is $23 per hour with an initial $15 setup fee. Which of the following equation represents the relationship between the total cost c in dollars, and the number of hours h, to rent the inflatable slide ?

(A)  c = 15 h     (B)  c = 23h      (C) c = 15h + 23

(D)  c = 23h + 15

Solution

(7)

-3x = y

(5x + y)² = 64

If (x, y) is a solution to the system of equations above, what is the value of xy ?

(A) -3       (B) -24      (C) -48      (D)  -96

Solution

(8) The function f is defined by f(x) = 5x² + 2x + 5. What is the value of f(2) ?

Solution

(9)

10 - 3 (x + 2) = 3x + 4

How many different values of x satisfy the equation above ?

(A) None       (B) One      (C) Two      (D)  More than two

Solution

(10) In the xy-plane, line l contains the point (1, 3) and has slope 2. Which of the following is an equation of line l ?

(A) y = 2x + 1       (B) y = 3x + 2     (C) y = 2x + 3

(D)  y = x + 2

Solution

(1) (16 + 5x) – (8 – 2x) =

(A)  8 + 3x  (B)  8 - 3x (C)  8 - 7x

(D)  8 + 7x (E)  24 - 7x

(2) The three lines shown intersect in a point.  The value of x

(A)  is 100.  (B)  is 80.  (C)  is 50.  (D)  is 20. 

(E)  cannot be determined from the given information

Solution

(3)  The straight line graph shows how many people are in a large cafeteria eating lunch at different times.  If the people leave at a steady rate, at what time will oly 150 people remain?

(A)  1:15 P.M.  (B)  1:30 P.M.  (C)  1:45 P.M. 

(D)  2:15 P.M.  (E)  3:30 P.M.

Solution

(4)  Two congruent circles have centers P and Q as shown.  What is the measure of angle PXQ?

(A)  30°  (B)  45°  (C)  55°  (D)  60°  (E)  75°

Solution

(5)  Andrew has d dollars.  He has one-third as many dollars as Bruce has.  Carlos has $80 less than half the total of Andrew’s and Bruce’s dollars.  In terms of d, how many dollars does Carlos have?

(A)  4d – 40  (B)  2d – 40  (C)  2d + 40 

(D)  2d + 80  (E)  2d – 80

Solution

(6) In the xy-plane, the graph of linear inequality contains the points (0, 2), (1, 1) and (4, 0). Which of the following could be the inequality ?

(A)  y ≤ (-1/2)x + 2  (B)  y ≥ (-1/2)x + 2  (C)  y ≤ -2x + 4 

(D)  y ≥ -2x + 4

Solution

(7) In 1947, milk cost $0.75 per gallon and bananas cost $0.15 per pound. Donna bought two gallons of milk and some bananas for a total of $2.25 in 1947. How many pounds of bananas did she buy?

Solution

(8)

4x - 5y = 24

x - 2y = 3

If (x, y) is the solution to the system of equations above, what is the value of x ?

Solution

(9) The length of line segment AB is 380. The length of line segment CD is 95% of the length of line segment AB. What is the length of line segment CD ? 

A) 285     B) 361    C) 380    D) 400

Solution

(10) The population density of Cedar County is 230 people per square mile. The county has a population of 85,100 people. What is the area, in square miles, of Cedar County?

Solution

(1)  The sum of 7 unequal positive integers is 61.  What is the largest possible value that any of those integers can have?

(A)  55  (B)  40  (C)  39  (D)  13  (E)  9

Solution

(2)  In the set {1, 5, x, 10, 15}, the integer x is the median.  The mean of the five numbers is one less than x.  The value of x is

(A)  6  (B)  7  (C)  8  (D)  9  (E)  none of these.

Solution

(3)  If 7/50 < 1/x < 8/51 where x is an integer, then x =

(A)  8  (B)  7  (C)  6  (D)  5  (E)  4

Solution

(4)  Half of 2⁸ is

(A)  2⁷ (B)  2⁶ (C)  2⁴ (D)  1⁸  (E)  8

Solution

(5)  If x is greater than 1/2 but less than 1, which of the following has the largest value?

(A)  2x – 1  (B)  x²  (C)  1/x  (D)  1 – x  (E)  x³ 

Solution

(6) For the function f, the graph of y = f(x) in the xy-plane has a slope of 3 and passes through the point (0, −8). Which equation defines f ?

A)  f(x) = 3x      B) f(x) = 3x - 8    C) f(x) = 3x + 5

D) f(x) = 3x + 11

Solution

(7)  The triangle shown has a perimeter of 22 units. If x = 9 units and y = 7 units, what is the value of z, in units?

A) 6      B) 7    C) 9    D) 16

Solution

(8) The function h is defined by h (x) = 3x − 7. What is the value of h(−2) ?

A) −13    B) −10    C) 10    D) 13

Solution

(9) The y-intercept of the graph of 12x + 2y = 18 in the xy-plane is (0, y). What is the value of y ?

Solution

(10) A model predicts that a certain animal weighed 241 pounds when it was born and that the animal gained 3 pounds per day in its first year of life. This model is defined by an equation in the form

f (x) = a + bx

where f(x) is the predicted weight, in pounds, of the animal x days after it was born, and a and b are constants. What is the value of a ?

Solution

(1)  Maria, Anoki, and Boris are teenagers, and the sum of their ages now is 49.  The sum of their ages 8 years from now will be F, and the sum of their ages 10 years ago was P.  The value of F – P is

(A)  54  (B)  18  (C)  17  (D)  6  (E)  2

Solution

(2)  If (1/4) + (1/x) = 1, then x =

(A)  1/8  (B)  2/3  (C)  4/3  (D)  2  (E)  3

Solution

(3)  When the integer N is divided by 7,  the quotient is Q and the remainder is 5.  When N + 24 is divided by 7, the remainder is ‘

(A)  4  (B)  3  (C)  2  (D)  1  (E)  0

Solution

(4)  Point B is on line segment AD, and point E is on line segment BC.  The value of x is

(A)  20  (B)  40  (C)  50  (D)  60  (E)  70

Solution

(5)  Three-fourths of a number is equal to L.  What is three-halves of that original number, in terms of L?

(A)  4/3L  (B)  3/2L  (C)  2L  (D)  3L  (E)  4L

Solution

(6)  7m = 5(n + p)

The given equation relates the positive number m, n and p. Which equation correctly gives n in terms of m and p ?

(A)  n = 5p/7m          (B)  n = (7m/5) - p

(C)  n = 5(7m) + p       (D)  n = 7m - 5 - p

(7) 

x + 2y = 6

x - 2y = 4

The solution to the given system of equations is (x, y). What is the value of x ?

A) 2.5       B) 5       C) 6      D) 10

(8)

The table shows the frequency of values in a data set

What is the minimum value of the data set?

(9) A number x is at most 17 less than 5 times the value of y. If the value of y is 3, what is the greatest possible value of x ?

10) In the figure shown, lines r and s are parallel, and line m intersects both lines. If y < 65 , which of the following must be true? 

A) x < 115   B) x > 115    C)  x + y < 180  D)  x + y > 180

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