In a right triangle, relative to angle A, the opposite side is 3 and the adjacent side is 4. What is sin A?
Hint
Opposite ÷ hypotenuse.
Independent Mastery Test · 261004
From First Principles
to Expert Problems.
50 multiple-choice questions. Start with the foundations. Build confidence. Finish with demanding mixed problems. Everything is written in English for independent study.
50 QUESTIONS10 MINUTESINSTANT FEEDBACKWRONG ANSWERS ONLY
A central angle measures 80°. What is the inscribed angle intercepting the same arc?
Hint
Inscribed angle = half central angle.
What is the mean of 4, 6, 8, 10, and 12?
Hint
Add all values and divide by the number of values.
For y = (x − 3)² + 2, what is the vertex?
Hint
Read p and q directly.
In a right triangle, relative to angle A, the opposite side is 5 and the hypotenuse is 13. What is cos A?
Hint
Find the adjacent side first.
An inscribed angle is 35°. What is the corresponding central angle?
Hint
Double the inscribed angle.
What is the median of 3, 7, 8, 10, 12, and 15?
Hint
For an even number of data points, average the two middle values.
What is the axis of symmetry of y = (x + 4)² − 1?
Hint
The axis is x = p in vertex form.
What is tan 45°?
Hint
At 45°, the two legs are equal.
A quadrilateral is cyclic. One angle is 112°. What is the opposite angle?
Hint
Opposite angles add to 180°.
What is the mode of 2, 4, 4, 5, 6, 6, 6, 8?
Hint
Mode = most frequent value.
What is sin 30°?
Hint
Remember the 30°–60°–90° triangle.
Two tangents are drawn from the same external point to a circle. If one tangent is 9 cm, what is the other?
Hint
Equal tangents theorem.
What is the minimum value of y = 2(x − 1)² − 5?
Hint
The vertex gives the minimum.
What is cos 60°?
Hint
Use the special-angle table.
For the data 2, 4, 6, 8, what is the mean?
Hint
Sum ÷ number of values.
A radius to a point of tangency is perpendicular to the tangent. If the angle between them is x, what is x?
Hint
Radius ⟂ tangent.
What is tan 60°?
Hint
Recall tan 60° = √3.
Which equation has vertex (−2, 3) and opens downward?
Hint
Match the vertex form.
The data are 2, 4, 6, 8, 10. What is the variance?
Hint
Square deviations, then average them.
If sin A = 3/5 for an acute angle A, what is cos A?
Hint
Complete the right triangle.
A chord is 10 cm long, and the perpendicular distance from the center to the chord is 12 cm. What is the radius?
Hint
Half the chord is 5.
For the data 2, 4, 6, 8, 10, what is the standard deviation?
Hint
Standard deviation = square root of variance.
Rewrite y = x² − 6x + 11 in vertex form.
Hint
Complete the square.
If tan A = 3/4 for an acute angle A, what is sin A?
Hint
Build a 3-4-5 triangle.
A circle has radius 10 cm. A chord is 12 cm long. What is the distance from the center to the chord?
Hint
Use the right triangle formed by the radius.
If every value in a data set increases by 5, what happens to the mean?
Hint
A constant added to every value shifts the mean by that constant.
What are the x-intercepts of y = x² − 5x + 6?
Hint
Factor the quadratic.
A cyclic quadrilateral has angles 2x and 3x as opposite angles. What is x?
Hint
Opposite angles sum to 180°.
A ladder 10 m long makes a 30° angle with the ground. How high does it reach?
Hint
Height is opposite the 30° angle.
A tangent and chord form an angle of 42°. What is the inscribed angle subtending the same chord on the opposite arc?
Hint
Tangent-chord angle equals the matching inscribed angle.
If every value in a data set increases by 5, what happens to the standard deviation?
Hint
Translation changes location, not spread.
A 12 m pole casts a shadow 12√3 m long. What is the sun's angle of elevation?
Hint
Use tan θ = height/shadow.
For y = −(x − 2)² + 9, what is the maximum value of y?
Hint
The vertex is the maximum.
Which data set is more consistent?
Hint
Smaller standard deviation means more consistent.
A cyclic quadrilateral has angles A = 3x + 10° and C = 5x − 30°. Find x.
Hint
Set opposite angles to 180°.
A triangle has sides 6 and 8 with included angle 30°. What is its area?
Hint
Use 1/2 ab sin C.
A parabola has vertex (4, −2) and passes through (5, 1). Which equation is correct?
Hint
Use the vertex form and the second point.
A scatter plot shows points rising from left to right in a tight pattern. What relationship is most likely?
Hint
Rising pattern = positive correlation.
A chord is 16 cm long. Its distance from the center is 6 cm. What is the radius?
Hint
Use a right triangle.
A parallelogram has adjacent sides 10 and 6 and included angle 30°. What is its area?
Hint
For a parallelogram, base × height = ab sin C.
Two tangents from point P touch a circle at A and B. If PA = 2x + 1 and PB = 11, what is x?
Hint
Set the two tangent lengths equal.
A scatter plot shows points falling from left to right. What relationship is most likely?
Hint
Falling pattern = negative correlation.
From a point on level ground, the angle of elevation to the top of a tower is 45°. If the point is 18 m from the tower, how high is the tower?
Hint
At 45°, opposite = adjacent.
A data set has mean 10. One new value, 20, is added and the new mean becomes 12. How many values were in the original set?
Hint
Set the old and new totals equal.
A central angle is 4x + 10°, and an inscribed angle intercepting the same arc is x + 20°. Find x.
Hint
Central angle is twice inscribed angle.
A 20 m cable reaches the top of a pole and makes a 60° angle with the ground. How tall is the pole?
Hint
Height = hypotenuse × sine.
A triangular field has sides 14 m and 10 m with an included angle of 30°. What is the field's area?
Hint
Use 1/2 ab sin C.
In a right triangle, cos A = 5/13. If the hypotenuse is 26, what is the side adjacent to A?
Hint
Multiply the hypotenuse by cos A.
A chord is 18 cm long and is 12 cm from the center. A second chord of the same circle is 10 cm from the center. Which is longer?
Hint
In the same circle, a chord closer to the center is longer.
Final Page · Answer Key
Answer Key
This page is intentionally last for clean printing.
01 A · 02 B · 03 C · 04 B · 05 B · 06 C · 07 C · 08 A · 09 C · 10 A · 11 C · 12 A · 13 B · 14 A · 15 A · 16 B · 17 C · 18 C · 19 B · 20 B · 21 B · 22 C · 23 B · 24 A · 25 C · 26 B · 27 C · 28 B · 29 B · 30 A · 31 B · 32 C · 33 A · 34 C · 35 A · 36 B · 37 A · 38 A · 39 A · 40 B · 41 B · 42 B · 43 B · 44 B · 45 A · 46 C · 47 B · 48 A · 49 A · 50 A