# Introduction to the Practice Exams

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1 Introduction to the Practice Eams The math placement eam determines what math course you will start with at North Hennepin Community College. The placement eam starts with a 1 question elementary algebra test and depending on your score the test may continue into either a college level or an arithmetic test to determine your final placement. You have the option to appeal your first score and retake the eam once. If neither score is what you want, you may retake the eam the net semester but once you enroll in a class, you may no longer take the placement eam. Look at the following flow chart to see a list of classes and their prerequisites. To move on to the net class you must complete the previous class with a C or better. You can see that your initial placement can make a big impact on the number of courses that you need to take. If you test into a lower class than you are qualified for you will have to spend at least one etra semester to get to the math class that you need. The following practice tests and answer keys are designed to give you an opportunity to study and review some concepts and skills that will be tested on the elementary algebra and arithmetic portions of the placement eam. The placement eam is a predictive test, so the specific questions asked will change each time the test is taken, but the practice eams cover the main concepts. Good Luck.

2 Arithmetic Practice Eam This practice eam has a selection of problems similar to those found on the Placement Eam at the Arithmetic Level. The actual eam is 17 questions long. After taking this practice eam, check your answers with the key to see detailed eplanations of the skills and steps needed to solve each problem. You may use scratch paper, but not a calculator. 1) 14 5 = a) -19 b) 11 c) -9 d) 9 ) a) 3 5 b) c) 3 5 d) 3 0 3) 9 0 = a) 4.5 b).18 c).45 d).09 4) Subtract the following fractions: 4 5 = 3 1 a) 1 b) c) 1 d) ) Find the product of 3 8 and 15. a) 1 0 b) 5 3 c) 6 3 d) 6 15

3 6) If a pot of soup is 3 full before lunch and 1 7 full after lunch, how much soup was used during lunch? a) 1 4 b) 1 1 c) 11 1 d) 1 7 7) Which of the following is not equivalent to 4 5? a).8 b) 8 5 c) 14 5 d) ) (.35) a).7 b).15 c) 1.5 d) 7 9) What percent of 30 is 6? a) % b) 0% c) 18% d) 5% 10) = a).03 b) 30 c) 30 d) ) = a) 10. b) 7.3 c) 7.9 d) 8.3 1) If a shirt costs \$4.47 and a pair of pants costs \$7.78, what is the cost if you buy both items?

4 a) \$5.5 b) \$51.45 c) \$41.5 d) \$ ) 1% of 78,456 is closest to: a) 00 b) 86,000 c) 160,000 d) 16,000 14) If 1 car weighs tons and 1 semi weighs 1 tons, what is the ratio of the weight of 5 cars to semis? a) : 5 b) 5 : c) 5 :1 d) 1: 6 15) If the length of a rectangle is 14 meters, and the width is 5 meters less than the length, what is the perimeter of the rectangle? a) 3 meters b) 46 meters c) 39 meters d) 70 meters

8 15) Answer: b) 46 Skills: Geometry problem To solve this geometry problem you need to know that the perimeter is the distance around the shape. If the width is 5 less than 14, then the width is 9 meters. Around a rectangle are two lengths and two widths, so the perimeter is. Helpful Site:

9 Elementary Algebra Practice Eam This practice eam has a selection of problems similar to those found on the Placement Eam at the Elementary Algebra Level. The actual eam is 1 questions long. After taking this practice eam, check your answers with the key to see detailed eplanations of the skills and steps needed to solve each problem. You may use scratch paper, but not a calculator. 1) Find the sum of 4 and 3. a) 1 b) 7 c) 7 d) 1 ) Find the value of 5 3( 6) 5 +. a) -80 b) 17 c) -5 d) 3 3) What is the product of 3 10 and? 5 7 a) 6 7 b) 7 c) d) 1 1 4) Subtract 5 6 from 7 4. a) 1 b) 1 1 c) 11 1 d) 3 5) If 5 3 =, find the value of. a) 5 b) 6 5 c) 15 d) 5 6

10 6) Find the value of a) 10 b) -4 c) 8 d) -10 7) Place the numbers in ascending order (from smallest to largest) ,,1, a),1,, b),,, c),,, d),,, ) What is the value of 3 y + y when = and y = 3? a) 9 b) 33 c) 6 d) 6 6 9) Simplify 9 a) b) c) 3 d) ) A rectangular garden is to be made with a perimeter of 54 meters. If the width is five meters less than the length, what are the dimensions of the garden? a) 4m by 30m b) 1m by 17m c) 6m by 9m d) 11m by 16m

11 11) ( a 3)( a 3) a) + = a 9 b) a 3a 9 + c) 3 5a 9 d) a 9a 6 1) Solve the equation: + 3 = 18 a) { 6,3} b) {, 9} c) { 4,3 } d) { 6, } 13) Find the sum of 3 + and 4 + a) b) + 8 c) d) < 14) Solve the inequality: 3( ) a) { < } b) 1 > c) > 15 8 d) 5 < 15) Simplify and add the radicals: a) 8 3 b) 10 c) 34 3 d) ) Evaluate 5 4 a) 10 b) 90 c) 16 d) 3

12 17) Which line has a slope of 1? a) b) c) d) 18) Subtract: 3 y a) y 3 y b) 3 y c) 3 y d) y 19) Two angles are supplementary. If the larger angle is 0 o more than three times the smaller, find the measure of each angle. o o a)85, 75 o o b) 40,140 o o c) 15,75 o o d) 60,10 0) Write the phrase the difference of a number and twice the square of a number as a simplified algebraic epression. a) 4 b) 3 c) d)

14 4) c) 11 1 Skills: Subtracting Fractions, Finding the Least Common Denominator, translating phrases. When the question asks you to subtract 5 6 from it means You need to know that to subtract (or add) fractions they need to have a common denominator. If you multiply the top and bottom of a fraction by the same value, you don t change the value of the fraction. So to create a common denominator, factor the denominators so you can see what factor(s) each fraction is missing, and add those missing factors. You can then subtract the numerators and put the answer over the common denominator = = = ) d) 5 6 Skills: Solving equations/fractions With equations we have the option to multiply (or divide) both sides by 5 any non-zero quantity or we can add (or subtract) both sides by the 3 = same quantity without changing the solutions. This is important since it allows us to rewrite equations in a form that we prefer. The best form is to 3 5 = 3 get the variable alone as in =, since then we can easily see the 3 solution. For this problem we can get the term alone by dividing both 5 1 sides by 3. = To divide the right side by 3, remember that dividing means 3 multiplying by the reciprocal. This gives us the solution. 5 = 6 Helpful site: 6) c) 8 Skills: Order of Operations, Absolute Value To evaluate this epression, we must first perform the operations inside of the absolute value symbols (just like parentheses). Remember that = the absolute value of a number represents the distance from that number to + 3 = zero so the absolute value is always positive. Make sure that you wait to add + 3 = the and the 3 until after you multiply the 3 because multiplication comes + 6 = before addition. 8 Helpful site:

15 7) d) 5, 11, 5, Skills: Fractions To compare fractions we need to create common denominators. The Least Common Denominator of all the fractions is 1. To convert the mied number to a fraction multiply the denominator by the whole number and add it to the numerator. The four fractions can then be grouped in the right order = = = = Helpful site: 8) b) 33 Skills: Evaluating epressions To evaluate an epression we must replace each variable with the given value. Be careful with negative values. The problem states that = and y = 3 so: ( ) ( )( 3) ( 3) 3 y + y = 3 + = = 33 Helpful site: 9) a) Skills: Factoring quadratics, simplifying rational epressions To simplify a rational epression you need to cancel any common factors (products). To see what the common factors are you need to factor the top and the bottom of the fraction. Only then can you see what factors are common and cancel them to get our final answer. Remember that quadratics often factor as the product of two binomials. For more help factoring polynomials see the web sites. 6 ( 3)( + ) ( + ) = = ( )( ) ( ) Helpful sites:

16 10) d) 11m by 16m Skills: Word problems, geometry formulas, equation solving To solve a word problem we need to translate it into an equation with variables. For this problem, the equation comes from the formula for the perimeter of a rectangle: P = l + w. We also know the relationship between the width and the length: w = l 5. To solve the problem we substitute the known quantities into the formula and solve the equation P = l + w ( 54) = l + ( l 5) Distribute the 54 = l + l 10 Add like terms 54 = 4l 10 Add 10 to each side 64 = 4 l Divide both sides by 4 16 = l Substitute into w = l 5 w = 16 5 w = 11 Helpful site: 11) b) a 3a 9 + Skills: Multiplying polynomials When you multiply two binomials together (like this problem) you should remember the FOIL method. This way of making sure that you find all of the products. It for First, Outer, Inner and Last. After you find the four products add any like terms to find the final answer. Helpful Site: ( a 3 )( a 3 ) F O I L a a + a 3 3 a 3 3 = a 6 a 3a 9 a + 3a 9 + = + = is a stands 1) a) { 6,3} Skills: Solving quadratics, factoring To solve a quadratic equation we need to get it in standard + 3 = 18 form a + b + c = 0, so subtract the 18 from both sides. Net = 0 we need to factor the epression. Remember that quadratics usually factor as two binomials and we can ( + 6)( 3) = 0 check our factoring by multiplying using the FOIL method + 6 = 0 3 = 0 to see that we haven t changed the equation. We can then set each factor to zero and then solve to find our two solutions. = 6 = 3 Helpful Site: 13) c) Skills: Combining like terms

19 equation that represents the information. If we let represent the smaller angle can solve the following equation. Once we know the value of we can find the other angle. ( ) ( ) = = = 160 = 40 3( 40) + 0 = 160 Helpful Site: Angle information 0) c) Skills: Translating epressions To translate a phrase into an epression you have to know which words turn into which symbols. In this problem difference means to subtract, a number means a variable, twice means to multiply by, and the square of a number means. Put it all together and you have. Helpful Site:

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