Practice Test History

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The length of a rectangle is 5 cm longer than its width. If the width is 12 cm, what is its perimeter?

**Instructions:** Read each problem carefully and write your answer in the box. Click next to solve more problems (up to 10), then click submit to get the results.

Note: Type ^2 for (²), ^3 for (³), ^deg for (°).

**eMath Challenge** is a good resource for students who wish to learn and improve their problem-solving abilities. It offers a wide range of math challenge problems whose solution methods are within the scope of primary mathematics.

The strategy is for the learner to take a series of practice tests on his or her own, with only a pen and scratch paper. The result of every test will be discussed with the coach, who will explain the correct analysis and solution to each wrong answer.

The following are the criteria that can be applied as filters to problem selection:

**Grade:**Grade I/II, Grade III, Grade IV, Grade V, Grade VI**Difficulty:**Easy, Average, Hard**Topic:**Any, Fraction, Percent, Ratio, Age, Amount, Discount/Gain, Interest, Distance, Rate/Speed, Angle, Perimeter, Area, Volume

You can't solve a math challenge problem if you can't add, subtract, multiply, or divide. Make sure that you have memorized the multiplication and addition tables up to 10x10 and 10+10.

Doing arithmetic calculations should be automatic and effortless. Subtraction and division are the inverse operations of addition and multiplication, respectively. So if you can add and multiply, you should also be able to subtract and divide.

Don't forget the rule of precedence by doing multiplication and division first before addition and subtraction. The order is from left to right, but the parenthesized expression always takes priority.

Addition Table

+ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |

4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |

5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |

8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |

10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

Multiplication Table

× | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |

3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |

4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 |

5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |

6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 |

7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 |

8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 |

9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |

10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

Identify what is asked, referred to as the "unknown," and which operation(s) to use by carefully reading the problem. Establish the relationships that exist between the given values and the unknown.

Read through the problem again to ensure nothing is missed. Interpret the problem based on real-life scenarios. A problem that is rightly understood is considered half-solved.

Use a standard formula if applicable, or create your own equation by translating the problem statement into a mathematical sentence. Take a hint on the given unit of measure. Develop the simplest solution and avoid a complicated approach.

In some cases, there could be another unknown that may require a preliminary solution. Do not assume anything that is not given.

Perform the required operations step-by-step until you arrive at the answer. Use the appropriate conversion factor to conform the given unit of measure to what is asked.

Simplify your answer to the lowest terms, and, whenever applicable, don't forget to append the unit of measure.

This is done by reversing the process. The answer becomes a given; then one of the given becomes the unknown.

Another way to check the answer is to redo the process, i.e., to solve the problem all over again. The answer should be the same; if not, review the process again. As you do this, be mindful of the allowed time and try not to exceed it. Find the balance between speed and accuracy.

- micro 1/1000000
- milli 1/1000
- centi 1/100
- deci 1/10
- deca 10
- hecto 100
- kilo 1000
- mega 1000000
- bi 2
- tri 3
- quad/tetra 4
- penta 5
- hexa 6
- hepta 7
- octa 8
- nona 9

- mm millimeter
- cm centimeter
- dm decimeter
- m meter
- km kilometer
- mg milligram
- g gram
- kg kilogram
- s second
- min minute
- h/hr hour
- ml milliliter
- l liter
- ha hectare

- 1 cm = 10 mm
- 1 dm = 10 cm
- 1 m = 10 dm or 100 cm
- 1 km = 1000 m
- 1 g = 1000 mg
- 1 kg = 1000 g
- 1 min = 60 s
- 1 h/hr = 60 min
- 1 ml = 1 cm³
- 1 l = 1000 ml or 1 dm³
- 1 ha = 10000 m²

Perimeter

- Triangle P = a + b + c
- Square P = 4s
- Rectangle P = 2(L + W)
- Circle C = 2πr or πD

- Triangle A = ½bh
- Square A = s²
- Rectangle A = LW
- Trapezoid A = ½h(b
_{1}+ b_{2}) - Circle A = πr²

- Cube V = s³
- Rectangular Prism V = LWH
- Circular Prism V = πr²h
- Prism (any) V = Ah, where A is area of the base
- Cone V = ⅓πr²h
- Sphere V = 4⁄3πr³
- Pyramid V = ⅓Ah, where A is area of the base

- ∠A + ∠B + ∠C = 180°

- ∑ = (n - 2) × 180°

- I = Prt

- ∑ = ½(n
_{1}+ n_{2})(n_{2}- n_{1}+ 1)

- ∑ = ½(n)(n + 1)

- ∑ = n(n + 1)

- ∑ = n²

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