New York City SHSAT 2017

In the figure above, points A, B, and C lie on the circumference of the circle centered at O. If ∠OAB measures 50º and ∠BCO meas ...

Line l has a slope of −2 and contains the point (4, −3). Which of the following points is also on line l? (F) (2, 1) (G) (3, 0 ...

In the circle with center O above, for what value of x does the circle have a circumference of 20π? (F) 5 (G) 10 (H) 15 (J) 20 ...

In the figure above, triangle XYZ has been divided into many smaller triangles, each of which is equilateral. If the area of tri ...

In the figure above, triangle PQO is an isosceles triangle with sides of lengths 5, 5, and 6. What is the area of rectangle MNOP ...

If ℓ 1 is parallel to ℓ 2 in the figure above, which of the following expressions must equal 180? I. a + b II. c + e III. c + ...

In the figure above, what is the value of a − b? (F) 7 (G) 30 (H) 37 (J) 107 (K) 148 ...

If the area of the circle centered at O is 36π and its diameter is x, then what is the circumference of a circle whose radius is ...

Note: Figure not drawn to scale. In the figure above, rectangle EFGH is inscribed in the circle with center Q and radius 13. If ...

Note: Figure not drawn to scale. Which of the following is the equation of a line that is perpendicular to the x-axis and four ...

(A) (B) 4 (C) (D) (E) 20 In the xy-plane, what is the area of a parallelogram with vertices (0, 0), (2, 0), (3, −2), and (5, −2 ...

...

Answers EXERCISE i. 20 ii. 135 iii. 35 iv. 60 v. 60 v. 5, 9 (The third side must be greater than 3 and less than 13.) vii. 16 vi ...

...

Answers and Explanations ...

PRACTICE SET E Since AB = BC = AC, triangle ABC is equilateral. Therefore, all of its angles are 60º. Since angle BCD, or x, is ...

The length of AC is represented by the expression 5 a − 2, so AC = 5(2) − 2 = 8. H The perimeter of a rectangle is 2(ℓ + w), whe ...

E To find the area of the frame, find the area of the frame and picture combined (the outer rectangle) and subtract from it the ...

D Circumference of a circle = 2πr, where r is the radius of the circle. So, a circle with a circumference of 36π has a radius of ...

a circle is πr^2 , so the area of circle P is π(5)^2 = 25π. B Note that the perimeter of the shaded region is in fact equal to t ...