The home of mathematics education in New Zealand.
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Problem Solving
This section of the nzmaths website has problem-solving lessons that you can use in your maths programme. The lessons provide coverage of Levels 1 to 6 of The New Zealand Curriculum. The lessons are organised by level and curriculum strand. Accompanying each lesson is a copymaster of the problem in English and in Māori.
Choose a problem that involves your students in applying current learning. Remember that the context of most problems can be adapted to suit your students and your current class inquiry. Customise the problems for your class.
- Level 1 Problems
- Level 2 Problems
- Level 3 Problems
- Level 4 Problems
- Level 5 Problems
- Level 6 Problems
The site also includes Problem Solving Information . This provides you with practical information about how to implement problem solving in your maths programme as well as some of the philosophical ideas behind problem solving. We also have a collection of problems and solutions for students to use independently.
- Solve equations and inequalities
- Simplify expressions
- Factor polynomials
- Graph equations and inequalities
- Advanced solvers
- All solvers
- Arithmetics
- Determinant
- Percentages
- Scientific Notation
- Inequalities
What can QuickMath do?
QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.
- The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
- The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
- The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
- The calculus section will carry out differentiation as well as definite and indefinite integration.
- The matrices section contains commands for the arithmetic manipulation of matrices.
- The graphs section contains commands for plotting equations and inequalities.
- The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.
Math Topics
More solvers.
- Add Fractions
- Simplify Fractions
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Math Questions Answers
In math questions answers each questions are solved with explanation. The questions are based from different topics. Care has been taken to solve the questions in such a way that students can understand each and every step.
1. Which is greater than 4? (a) 5, (b) -5, (c) -1/2, (d) -25. Solution: 5 greater than 4. Answer: (a)
2. Which is the smallest? (a) -1, (b) -1/2, (c) 0, (d) 3. Solution: The smallest number is -1. Answer: (a) 3. Combine terms: 12a + 26b -4b – 16a. (a) 4a + 22b, (b) -28a + 30b, (c) -4a + 22b, (d) 28a + 30b. Solution: 12a + 26b -4b – 16a. = 12a – 16a + 26b – 4b. = -4a + 22b. Answer: (c) 4. Simplify: (4 – 5) – (13 – 18 + 2). (a) -1, (b) –2, (c) 1, (d) 2. Solution: (4 – 5) – (13 – 18 + 2). = -1-(13+2-18). = -1-(15-18). = -1-(-3). = -1+3. = 2. Answer: (d) 5. What is |-26|? (a) -26, (b) 26, (c) 0, (d) 1 Solution: |-26| = 26. Answer: (b)
Solution: 3y(x – 3) -2(x – 3). = (x – 3)(3y – 2). Answer: (c). 9. Solve for x: 2x – y = (3/4)x + 6. (a) (y + 6)/5, (b) 4(y + 6)/5, (c) (y + 6), (d) 4(y - 6)/5. Solution: 2x – y = (3/4)x + 6. or, 2x - (3/4)x = y + 6. or, (8x -3x)/4 = y + 6. or, 5x/4 = y + 6. or, 5x = 4(y + 6). or, 5x = 4y + 24. or, x = (4y + 24)/5. Therefore, x = 4(y + 6)/5. Answer: (b).
11. Find the value of 3 + 2 • (8 – 3) (a) 25, (b) 13, (c) 17, (d) 24, (e) 15. Solution: 3 + 2 • (8 – 3) = 3 + 2 (5) = 3 + 2 × 5 = 3 + 10 = 13 Answer: (d)
15. What is the radius of a circle that has a circumference of 3.14 meters? Solution: Circumference of a circle = 2πr. Given, circumference = 3.14 meters. Therefore, 2πr = Circumference of a circle or, 2πr = 3.14. or, 2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14]. or, 6.28r = 3.14. or, r = 3.14/6.28. or, r = 0.5. Answer: 0.5 meter. If students have any queries regarding the questions given in the math questions answers, please fill-up the below comment box to convey your message, so that we can help you.
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