Lesson 1- Lectures (Basic Math Skills) – SAT, SHSAT & BCA Test Prep

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The “Lectures” page at the start of each lesson chapter provides general material about the content of each lesson chapter followed by specific topic lessons. Topic lessons include video and written tutorials and related exercises to practice the focused skill and then SHSAT level problems to execute the skill in combination with other skills in more realistic SHSAT problems.

TestPrepSHSAT

TestPrepSHSAT

VIDEO TUTORIAL:

Math Basics Instruction Unit - Part A

Math Basics Instruction Unit - Part B

These instructional quizzes are short, limited to only about a dozen questions, and they are not graded or timed. Occasionally there will be a question introducing a topic that you are not expected to answer at first. Do not panic. The instructional material will likely be introduced in the following answer explanation. The purpose of these instructional modules is to review subject material by topic that you will likely encounter on the exam and provide some topic specific tips to improve your ability to solve related problems.

WHICH OF THE FOLLOWING IS NOT AN IRRATIONAL NUMBER?

$\displaystyle \pi$

$\displaystyle e$

$\displaystyle i$

$\displaystyle \sqrt{2}$

Which of the following is not a rational number?

1/3

22/7

-3

Which one of these numbers is real?

i²

i³

$\displaystyle \infty$

Complex numbers can be expressed in the form a + bi where a and b are variables that represent some unknown value. If a complex number is a combination of part real numbers and part imaginary numbers, then which of the following is not a complex number?

$\displaystyle i\sqrt{6}$

-4

2 - 6i

They're all complex numbers

The product of two imaginary numbers is always:

A real number

An imaginary number

A rational number

An irrational number

The following product must be:

23·x⁴·y²·(-7)·14·(-21)·3

Even

Odd

Negative

None of the above

|-12| × -|2 - 5| ÷ |-6|^{2 = ?}

-3

-1

What is the result of the quotient 3!/2! ?

3/2!

(3/2)!

(3-2)!

Math Basics Instruction Unit - Part C

Math Basics Instruction Unit - Part D

It is 62° at noon. The temperature drops 3° every hour for 16 hours. What is the correct expression for the temperature at midnight?

62 - 3 × 16

62 + 3 × 16

62 - 3 × 12

62 - 12

What is the square of -9?

-81

-18

6 ÷ 3 - 4 × -2 = ?

-6

-12

What is the positive difference between the following expression with and without parentheses?

(6 - 3) × 3 ÷ (4 - 2)

19/2

11/4

-1/2

25/4

Math Basics Instruction Unit - Part E

Can you find the sum (37+ 27) + 73 without using a calculator? What property or law of algebra did you use?

110 - associative

137 - distributive

110 - commutative

137 associative

56 × 33 - 33 × 36 = ?

128

330

660

760

Can you convert the decimal number 84 to binary?

Hint: Our number system is base 10 and each figure represents the product between that figure and the next higher power of 10. e.g. 84 = 8 × 10¹ + 4 × 10⁰ = 80 + 4. Binary is a base 2 number system with only two possible figures, 1 and 0.

1010100

1011000

0101010

1010010

If x and y are any two real numbers, the operation ♣ is defined by
x♣y = xy + 9. For example, 2 ♣ 3 = 2 × 3 + 9 = 6 + 9 = 15.

The operation ♣ adheres to which of the following laws?

Associative

Commutative

Distributive over addition

Distributive over multiplcation

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