Upper Level · All Topics · Real Exam Format
Number concepts tested on the SSAT include prime numbers, factors, multiples, divisibility, fractions, decimals, percentages, ratios, exponents, and square roots.
MEMORIZE First 15 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
MEMORIZE Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
MEMORIZE Divisibility: ÷3 → digit sum divisible by 3; ÷9 → digit sum divisible by 9; ÷4 → last two digits divisible by 4
What is the LCM of 12 and 18?
GCF(12,18) = 6 → LCM = (12 × 18) ÷ 6 = 36
Which of the following numbers has exactly three distinct positive factors?
If 2x = 64 and 3y = 27, what is the value of x − y?
A jacket originally costs $80. It is first discounted by 25%, then the sale price is increased by 20%. What is the final price?
The GCF of two numbers is 6 and their LCM is 90. One of the numbers is 18. What is the other number?
Algebra on the SSAT covers linear equations, inequalities, systems of equations, polynomials, factoring, quadratics, and function notation.
MEMORIZE Slope-intercept: y = mx + b (m = slope, b = y-intercept)
MEMORIZE Standard form: ax + by = c; Vertex of parabola: x = −b/(2a)
Solve: 3x − 7 = 14 → 3x = 21 → x = 7
If 4(2x − 3) = 5x + 6, what is the value of x?
If 2x + y = 10 and x − y = 2, what is the value of x?
Which of the following is the solution to −3x + 9 > 0?
What are the roots of x² − 5x + 6 = 0?
If f(x) = 3x² − 2x + 1, what is f(−2)?
Geometry topics include area, perimeter, volume, angles, triangles (Pythagorean theorem), circles, coordinate geometry, and similar figures.
MEMORIZE Special right triangles: 3-4-5, 5-12-13, 8-15-17, 30-60-90 (1:√3:2), 45-45-90 (1:1:√2)
MEMORIZE Sum of interior angles of n-gon = (n−2) × 180°
A right triangle has legs 6 and 8. Hypotenuse = √(36+64) = √100 = 10
A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?
A circle has a circumference of 10π. What is the area of the circle?
Two parallel lines are cut by a transversal. One co-interior (same-side interior) angle measures 70°. What is the measure of the other co-interior angle?
A rectangular box has length 5, width 4, and height 3. If all dimensions are doubled, by what factor does the volume increase?
What is the distance between points (1, 2) and (4, 6)?
Data analysis covers mean, median, mode, range, probability, combinations, permutations, and reading graphs/tables.
MEMORIZE Median = middle value when data is sorted (average of two middle if even)
MEMORIZE P(A or B) = P(A) + P(B) − P(A and B)
Data: {3, 7, 7, 9, 12} → Mean = 38/5 = 7.6; Median = 7; Mode = 7
The average (mean) of five numbers is 12. If four of the numbers are 8, 10, 14, and 16, what is the fifth number?
A bag contains 4 red, 3 blue, and 5 green marbles. If one marble is drawn at random, what is the probability of drawing a blue or green marble?
How many different 3-person committees can be formed from a group of 7 people?
Word problems require translating real-world situations into math. Key areas: rate × time = distance, work problems, mixture problems, age problems, ratio problems.
MEMORIZE Two people working together: time = (a×b)÷(a+b)
MEMORIZE Age problems: write equations for NOW, then apply change (+n or −n years)
Car travels 120 miles at 40 mph. Time = 120 ÷ 40 = 3 hours
Train A travels at 60 mph and Train B travels at 90 mph in the same direction. Train A has a 1-hour head start. How many hours after Train B departs will Train B catch Train A?
Alice can paint a fence in 6 hours; Bob can paint the same fence in 3 hours. If they work together, how many hours will it take to paint the fence?
Sarah is 3 times as old as her daughter Emma. In 4 years, Sarah will be twice as old as Emma. How old is Emma now?
Detailed solutions for all 20 questions