TheoryGACE Study Guide
Study for the GACE with exam topics, practice questions, a free PDF, video walkthrough and timed mock exam links.
How to study for GACE
- Read the topic list so you know what the exam is likely to cover.
- Answer the free practice questions and read every explanation.
- Download the PDF for offline review.
- Use timed mock exams when your untimed practice feels comfortable.
Topics to review
- The core topics and terminology you'll be tested on
- Rules, standards and best-practice procedures
- Real-world scenarios and how to respond
- Common mistakes and how to avoid them
Try GACE questions now
Q1Which symbol most accurately reflects the relationship between the two numbers below?<br/><br/><tex>1.2</tex> ☐ <tex>\frac{9}{10}</tex>
Show answer
✓ Correct answer: >
Option A: Since the numerator (9) is less than the denominator (10) of the fraction, it is less than 1. Therefore, 1.2 is greater than <tex>\frac{9}{10}</tex>.<br/><br/>Option C: Since the numerator (9) is less than the denominator (10) of the fraction, it is less than 1.0.
Q2Shane’s Softball Production Company can produce 12 softballs in an hour. How many softballs can they produce in 14 hours?
Show answer
✓ Correct answer: 168
Although this is not a difficult problem, and could be calculated mentally, perhaps by multiplying 14 by 10 (140), then adding 2 more 12s to the answer.<br/><br/>However, there is a trick that allows you to multiply numbers close to ten together within seconds.<br/><br/>First, consider the problem: 14 x 12<br/>Using the 2 in 12, add it to 14: 16 (these are the first two digits of the answer).<br/>Using the 2 in 12, multiply it by the 4 in 14: 8 (this is the last digit of the answer).<br/>Thus, the answer to 14 x 12 is 168.<br/><br/>It works for larger numbers in the teens, but those involve “carrying”.<br/>Consider the problem: 17 x 14.<br/>Using the 4 in 14, add it to 17: 21<br/>Using the 4 in 14, multiply it by the 7 in 17 (28). The 8 is the last digit of the answer. Carry the 2 over, and add it to the 21 from the previous step to get 23. The answer to 17 x 14 is 238.<br/><br/><b>Key Takeaway:</b> Sometimes you will find it necessary to multiply numbers in the teens together. With practice, this strategy will allow you to perform that calculation mentally, both quickly and accurately.<br/><br/>Again, this is a trick that requires lots of practice that works for some, and doesn’t work for others.
Q3Students are plotting points on a coordinate plane. Rudy plots the point <tex> (-6, 3) </tex> in the second quadrant. Frank plots the same point in the third quadrant. Who plotted the point correctly?
Show answer
✓ Correct answer: Rudy
When writing coordinate pairs, we always write the <tex> x- </tex>coordinate first, then the <tex> y- </tex>coordinate. <tex> (x, y)</tex> Quadrants on a graph are numbered <em>counter-clockwise</em> as shown here:<br/><br/><img src="asset:assets/questions/50f583651cc758df.jpeg"><br/><br/><em>Retrieved from: https://openstax.org/books/prealgebra-2e/pages/11-1-use-the-rectangular-coordinate-system</em> The point <tex> (x, y) </tex> falls in the first quadrant, where both the points are <em>positive</em>. In the second quadrant, the <tex> x- </tex>coordinate is <em>negative</em> and the <tex> y- </tex>coordinate is <em>positive</em> ( <tex> (-x,y) </tex>). In the third quadrant, the <tex> x- </tex>coordinate is <em>negative</em> and the <tex> y- </tex>coordinate is also <em>negative</em> ( <tex> (-x,-y) </tex>). In the fourth quadrant, the <tex> x- </tex>coordinate is <em>positive</em> and the <tex> y- </tex>coordinate is <em>negative</em> ( <tex> (x,-y) </tex>). The point <tex> (-6,3) </tex> is in the second quadrant since the <tex> x- </tex>coordinate is negative and the <tex> y- </tex>coordinate is positive. Thus, <em>Rudy</em> plotted the point correctly.
Q4Sharon bought an equal number of $65, $55, and $40 tickets for a concert. She spent $640 for all the tickets. How many of each did she buy?
Show answer
✓ Correct answer: 4
Let's use <em>x</em> to represent the number of tickets bought at each price. Then we can say 65<em>x</em> + 55<em>x</em> + 40<em>x</em> = 640. If we add the numbers on the left side of the equation, we get 160<em>x</em> = 640. To find the value of <em>x</em>, divide both sides of the equation by 160. <em>x</em> = 4.
Q5The price of a shirt is increased by 20%, and the price of a $40 pair of shoes is decreased by 40%. If the new price of the shirt now equals the new price of the shoes, what was the original price of the shirt?
Show answer
✓ Correct answer: $20
First, determine the new price of the shoes: 40% of $40 is (40/100) · $40 = $16, so the new price of the shoes is $40 − $16 = $24. At this point, we can work with the answers to figure out which one is correct: increase each answer by 20% until we get $24. The correct answer is B since 20% of $20 is $4 and $20 + $4 = $24.
Q6What is the term for the distance around a circle?
Show answer
✓ Correct answer: Circumference
The distance around a circle is its circumference.
Full GACE bank + unlimited mocks
Try 30 questions free. Unlock the complete GACE question bank, every explanation, and unlimited timed mock exams. Practice on any device.
Unlock GACE →