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Study on the flySATPractice testMath — Module 1

SAT

SAT Math — Module 1 practice test

  • 22 questions
  • 35 minutes
  • Nothing is deducted for a wrong answer
  • Free

The Math — Module 1 section of the SAT practice test — 22 questions. Mark your answers, then press Finish at the bottom to see your score.

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Question 1

xp(x)0413203−5

The table shows values of the quadratic function pp for four values of xx. What is the value of p(4)p(4)?

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Answer: -12

The second differences of p(x)p(x) are constant at −2-2, so p(x)=−x2+4p(x)=-x^2+4 and p(4)=−12p(4)=-12.

Question 2

For the linear function rr, the graph of y=r(x)y=r(x) in the xyxy-plane has a slope of −2-2, and r(1)=8r(1)=8. Which equation defines rr?

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Answer: A — r(x)=−2x+10r(x)=-2x+10

Write r(x)=−2x+br(x)=-2x+b and use r(1)=8r(1)=8: 8=−2(1)+b8=-2(1)+b, so b=10b=10.

Question 3

Which expression is equivalent to 9m+4m+7n9m + 4m + 7n?

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Answer: C — 13m+7n13m + 7n

Combine the like terms in m: 9m + 4m = 13m. The 7n term has no like term to combine with, so it stays as is: 13m + 7n.

Question 4

q2−5q−24=0q^2-5q-24=0

What is the lesser solution to the given equation?

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Answer: -3

Factor as (q−8)(q+3)=0(q-8)(q+3)=0, so q=8q=8 or q=−3q=-3; the lesser solution is −3-3.

Question 5

5(x+3)=405(x+3)=40

Which equation has the same solution as the given equation?

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Answer: A — x+3=8x+3=8

Dividing both sides of 5(x+3)=405(x+3)=40 by 5 gives x+3=8x+3=8, so that equation has the same solution. x+3=40x+3=40 skips the division by 5; x+3=35x+3=35 subtracts 5 from 40 instead of dividing; x+3=−8x+3=-8 uses the wrong sign.

Question 6

A 45∘45^\circ-45∘45^\circ-90∘90^\circ triangle has legs of length 14. What is the length of the hypotenuse?

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Answer: C — 14214\sqrt2

The hypotenuse equals a leg times 2\sqrt2, giving 14214\sqrt2.

Question 7

8,10,11,13,8, 10, 11, 13, and xx

The mean of the five values in the data shown is 12. What is the value of xx?

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Answer: A — 18

The required total is 5(12)=605(12)=60; the four known values sum to 42, so x=18x=18.

Question 8

A candle decreases in height by 0.5 inches every 2 hours as it burns. If the candle has burned for 8 hours and is now 6 inches tall, what was the candle’s original height, in inches?

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Answer: C — 8

In 8 hours, the candle burns down by 0.5×(8/2)=20.5\times(8/2)=2 inches. Original height =6+2=8=6+2=8 inches.

Question 9

There are 400 trees in a park. Of these trees, 8%8\% are oak trees. How many of the trees in the park are oak trees?

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Answer: 32

400×0.08=32400\times 0.08=32.

Question 10

A delivery cart can carry at most 94 kilograms of crates and parcels. Each crate weighs 12 kilograms, and each parcel weighs 5 kilograms. The cart must carry at least 5 parcels. If cc is the number of crates and pp is the number of parcels, which ordered pair (c,p)(c,p) represents a load the cart can carry?

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Answer: C — (5,6)(5,6)

An allowable load satisfies 12c+5p≤9412c+5p\le94 and p≥5p\ge5. For (5,6)(5,6), the total weight is 12(5)+5(6)=9012(5)+5(6)=90 kilograms and there are 6 parcels. (3,12)(3,12) weighs 12(3)+5(12)=9612(3)+5(12)=96 kilograms, (4,10)(4,10) weighs 12(4)+5(10)=9812(4)+5(10)=98 kilograms, and (6,4)(6,4) has fewer than 5 parcels.

Question 11

A tree nursery recorded the number of years after several trees were planted and each tree’s trunk diameter, in centimeters. The scatterplot and a line of best fit are shown.

2468101214510152025Years after plantingTrunk diameter(centimeters)

Which use of the line of best fit would be an interpolation rather than an extrapolation?

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Answer: C — Predicting the trunk diameter 5 years after planting

The observed xx-values range from 1 to 9 years. A prediction at 5 years is within this range and is therefore an interpolation; the other predictions are beyond the observed range.

Question 12

The function gg is defined by g(x)=2(x−3)2−8g(x)=2(x-3)^2-8. What is the yy-coordinate of the yy-intercept of the graph of y=g(x)y=g(x)?

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Answer: D — 10

The yy-intercept occurs when x=0x=0. Evaluating gives g(0)=2(0−3)2−8=18−8=10g(0)=2(0-3)^2-8=18-8=10.

Question 13

3x−y=43x-y=4

The given equation is one equation in a system of two linear equations. Which equation would result in the system having infinitely many solutions?

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Answer: A — 6x−2y=86x-2y=8

The first choice is exactly twice the original equation, so both equations describe the same line.

Question 14

2(3x−y)=5y+142(3x-y)=5y+14

When the given equation is solved for yy, the result has the form y=px+ry=px+r. What is the value of pp?

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Answer: C — 67\dfrac{6}{7}

Expanding and collecting the yy-terms gives 6x−2y=5y+146x-2y=5y+14, so 7y=6x−147y=6x-14. Therefore, y=67x−2y=\dfrac{6}{7}x-2 and p=67p=\dfrac{6}{7}.

Question 15

A right circular cylinder has a volume of 540 cubic inches. The area of the base of the cylinder is 36 square inches. What is the height, in inches, of the cylinder?

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Answer: A — 15

Volume of a cylinder is V=BhV = Bh. Substituting the given values yields 540=36h540 = 36h, so h=15h = 15.

Question 16

uvw92°(6x-4)°

In the figure shown, line ww intersects parallel lines uu and vv. What is the value of xx?

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Answer: A — 16

Angles 3 and 7 are corresponding angles, so they are equal: 6x−4=926x-4=92, giving 6x=966x=96 and x=16x=16.

Question 17

In a circle, inscribed angle ∠ABC\angle ABC intercepts arc ACAC and measures 38∘38^\circ. What is the measure, in degrees, of arc ACAC?

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Answer: C — 76∘76^\circ

An inscribed angle is half its intercepted arc, so arc AC=2(38∘)=76∘AC=2(38^\circ)=76^\circ.

Question 18

Which expression is equivalent to 7x−2−3x+2\dfrac{7}{x-2}-\dfrac{3}{x+2}, where x≠2x\ne2 and x≠−2x\ne-2?

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Answer: C — 4x+20x2−4\dfrac{4x+20}{x^2-4}

Find a common denominator: 7(x+2)−3(x−2)(x−2)(x+2)=7x+14−3x+6x2−4=4x+20x2−4\dfrac{7(x+2)-3(x-2)}{(x-2)(x+2)}=\dfrac{7x+14-3x+6}{x^2-4}=\dfrac{4x+20}{x^2-4}.

Question 19

2n2−9n−35=02n^2 - 9n - 35 = 0

What is the positive solution to the given equation?

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Answer: C — 7

Factoring gives (2n+5)(n−7)=0(2n+5)(n-7)=0, so n=−52n=-\dfrac{5}{2} or n=7n=7; the positive solution is 7.

Question 20

A repair shop charges a flat fee of $35 plus $12 per hour. After a $17 coupon was applied to the total charge, Mira paid $90. For how many hours was Mira charged?

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Answer: 6

Let hh be the number of hours. Then 35+12h−17=9035 + 12h - 17 = 90, so 18+12h=9018 + 12h = 90, 12h=7212h = 72, and h=6h = 6.

Question 21

xA(x)B(x)03485333

The table gives values of two linear functions, AA and BB. For what value of xx does A(x)=B(x)A(x) = B(x)?

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Answer: 3

A(x)=6x+3A(x)=6x+3 and B(x)=−9x+48B(x)=-9x+48 from the table; setting them equal: 6x+3=−9x+486x+3=-9x+48 gives 15x=4515x=45, so x=3x=3.

Question 22

The graph of y=f(x)y=f(x) is shown, where f(x)=a(b)x+cf(x)=a(b)^x+c and aa, bb, and cc are constants. The dashed line is an asymptote, and the marked points lie on the graph. Which equation defines ff?

−112345−112345678xy(0, 6)(1, 4)
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Answer: C — f(x)=4(12)x+2f(x)=4\left(\dfrac{1}{2}\right)^x+2

The dashed line is the horizontal asymptote y=2y=2, so c=2c=2. The point (0,6)(0,6) gives a+c=6a+c=6, so a=4a=4. The point (1,4)(1,4) gives 4b+2=44b+2=4, so b=12b=\dfrac{1}{2}. Therefore f(x)=4(12)x+2f(x)=4\left(\dfrac{1}{2}\right)^x+2.

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