Common Core Grade 7 Part 1 Review Test

1. Examine the figure below.

If the triangle is dilated past a scale factor of ii, what is the perimeter of the new triangle?

1. 19
2. 32
3. 44
4. 76

2. Examine the figures below.

What calibration factor was used to scale the rectangle?

1. ¼
2. ¹/_iii
3. 3
4. 4

three. Which of the following sets of angles CANNOT exist used to construct a triangle?

1. Iii acute angles
2. 2 acute angles and ane right bending
3. Two acute angles and one obtuse angle
4. 2 right angles and one acute angle

4. If the correct rectangular prism shown beneath was horizontally sliced, which of the post-obit shapes would BEST depict the resulting two-dimensional shape?

1. Parallelogram
2. Rectangle
3. Rhombus
4. Square

5. Kevin is planting vegetables in his garden. If the garden is in the shape of a circle with a diameter of 10 feet, what is the area of the garden?

1. 15.7 ft2
2. 31.iv ft2
3. 78.five ft2
4. 314 ft2

6. Tory went to see a Monster Truck show at the local arena. Before the prove, Tory got to see the trucks up shut. He noticed that each monster truck tire had a radius of about iii ft. Based on that radius, what would exist the distance around each tire?

1. nine.42 ft
2. 18.8 ft
3. 28.iii ft
4. 113 ft

7. Examine the effigy below.

What is the value of x?

1. 4
2. 6
3. 15
4. 21

8. What is the measure of ?DBC?

1. 10°
2. xx°
3. 40°
4. l°

9. Jason is building a desk for his bedroom. He wants the desk to fit in the corner of his room and decides to become with a trapezoid design. If Jason uses the dimensions shown in the picture below, how many square feet of plywood volition he demand to build the desk height?

1. 5 ft2
2. 6 ft2
3. 9 ft2
4. 12 ft²

x. Natalie recently bought a jewelry box, but she wants to re-cover the box with a more colorful textile. If the jewelry box is a cube with sides eight cm long, how much fabric will Natalie need in order to cover all sides of the box?

1. 64 cm²
2. 192 cm²
3. 384 cm²
4. 512 cmⁱⁱ

Answers and Explanations

---

1. D: Since the original triangle is dilated past a calibration factor of 2, the length of each side volition be multiplied past 2 to become the side lengths of the new triangle. Therefore, 8×2=16, 12×2=24, and 18×2=36. Then, sixteen+24+36=76. Answer A results if each of the side lengths was incorrectly divided by 2. Respond B results if 2 was incorrectly subtracted from each of the side lengths. Respond C results if 2 was incorrectly added to the length of each side.

2. A: To make up one's mind the calibration cistron, accept the side lengths of the scaled rectangle and split up them by the corresponding sides of the original rectangle:¹/₄=ⁱ/₄ and³/₁₂=^ane/_four. Therefore, the scale factor used to scale the rectangle is 1/4. Answer B results if the scale factor was incorrectly adamant by dividing the sides inside each rectangle in the order of⁴/₁₂=¹/₃and¹/_iii=¹/₃. Answer C results if the scale factor was incorrectly adamant by dividing the sides inside each rectangle in the order of¹²/₄=iii and³/_one=iii. Answer D results if the scale cistron was incorrectly gear up to have the original side lengths divided by the values of the scaled side lengths:¹²/₃=4 and⁴/₁=4.

three. D: In order to construct a triangle, the 3 angles must sum to 180°. In Reply D, the 2 right angles past themselves would sum to180°, so calculation an acute angle to that value would brand the sum greater than 180°. Therefore, a triangle cannot exist synthetic with two right angles. Answers A, B, and C are all possible angle options for constructing a triangle.

iv. D: Horizontally slicing the right rectangular prism would create slices that are parallel to the base of the prism. Since the base of the prism is a square with sides of length iv, each of the horizontal slices would besides be in the shape of a foursquare. Answers A and C are the shapes that the base appears to be if 1 does non take into account the drawing of the 3-D prototype and that the prism is a right rectangular prism. Answer B is the resulting two-dimensional shape if the prism was vertically sliced.

5. C: The formula for the area of a circumvolve is A=pr². Since the diameter of the garden is 10 ft, the radius of the garden is 5 ft. Therefore, A=three.14(five "ft" )ⁱⁱ=78.5″ft"². Answer A is the consequence if the radius was not squared, i.due east. ?r. Answer B is the result if the circumference of the garden was calculated. Respond D is the result of using the diameter in the area formula.

6. B: The distance around each tire is the circumference of the circumvolve: C=2pr=ii(iii.xiv)(iii "ft" )=18.84 "ft" . Answer A is the result if the radius was not doubled. Answer C is the area inside of the tire. Answer D is the result if the diameter was used in the area formula.

7. C: The two angles shown in the figure are supplementary. In club to solve for x, the following equation must be used: 10x-5+35=180. This equation simplifies every bit: 10x+30=180. After subtracting thirty from both sides, the equation becomes 10x=150. Finally, after dividing both sides by 10, the solution is ten=15. Answer A results from treating the angles every bit congruent and setting up the equation as 10x-five=35. Reply B results from treating the angles as complementary and setting upward the equation equally 10x-5+35=90. Answer D results if the equation was correctly gear up up as 10x+30=180, but then 30 was incorrectly added to both sides to get 10x=210.

8. C: Before nosotros tin observe measure of ?DBC, we first need to solve for 10. Since ?ABD and ?DBC are complementary, we need to apply the equation m ?ABD + grand ?DBC = xc. Substituting for the values of g ?ABD and m ?DBC, the equation becomes 5x+4x=90. This equation simplifies as 9x=90. Finally, afterward dividing both sides of the equation by ix, the result isx=10. To find the measure ?DBC, we substitute x=x into (4x)° to become (iv(10))°=40°. Reply A is the value of 10. Answer B is the value of x if the angles were treated as supplementary and ready as 5x+4x=180. Reply D is the measure of ?ABD.

9. B: The formula for the surface area of a trapezoid is A=1/2 h(b_1+b_2), where h is the pinnacle, and b1 & b2 are lengths of the two bases. Therefore, A=one/ii (2 "ft" )(five "ft" +1 "ft" )=i/2 (2 "ft" )(half-dozen "ft" )=6 ?"ft" ?^2. In Reply A, only the 5 ft base of operations was used in the calculation. In Reply C, the 3 ft value was used for the height. In Answer D, the 1/two was left out of the formula, so the surface area was incorrectly calculated as A=h(b_1+b_2).

ten. C: The amount of material needed to comprehend the jewelry box is equal to the area of the box. The formula for the expanse of a cube is SA=6², where s is the length of one side. Therefore, the area of the jewelry box is SA=six(8 cm )²= half dozen(64cm)² =384 cm^two. In Reply A, the area of merely one side of the box was calculated. In Answer B, the perimeter of one side of the box was multiplied past 6. In Answer D, the book of the box was calculated.

saldanashink1999.blogspot.com

Source: https://www.testprepreview.com/math-grade-7.htm

Share this post