Grade 10 · Math

Grade 10 math

Grade 10 math is where quadratics arrive: expanding, factoring, and the parabolas they make. Trigonometry starts too. Here is what the year covers, where students usually get stuck, and one way to help.

What your teen learns this year

Courses differ by province and state, but most grade 10 math covers:

  • Quadratics. Expanding and factoring, solving quadratic equations, and graphing parabolas.
  • Systems of equations. Where two lines cross, by graphing, substitution or elimination.
  • Analytic geometry. Distance, midpoint and slope on a grid.
  • Trigonometry. Sine, cosine and tangent in right triangles, and similar triangles.
  • Exponents and measurement. Exponent laws and radicals; the western provinces add measurement units and functions.

Ontario's grade 10 math is an academic course (MPM2D) or an applied one (MFM2P). The western provinces teach a grade 10 course that leads into their Foundations and Pre-calculus paths, and in much of the US grade 10 is a geometry course.

Where kids usually get stuck

  1. 1Mixing up the signs when factoring. x² − 2x − 15 is (x + 3)(x − 5), not (x − 3)(x + 5): the pair has to add to −2 as well as multiply to −15.
  2. 2Squaring a bracket term by term. (x + 3)² is not x² + 9. It is x² + 6x + 9: the middle term is easy to lose.
  3. 3Labelling the triangle from the wrong angle. Opposite and adjacent depend on which angle you are working from. Mark the angle first.

One of Pip's tricks

Sum and product

Use it when factoring x² + bx + c, like x² + 7x + 12 or x² − 2x − 15.

  1. Look for two numbers that multiply to c and add to b.
  2. List the factor pairs of c with their signs: if c is negative, the pair has one positive and one negative.
  3. Write (x + first)(x + second) and expand it to check.

Watch it work. x² − 2x − 15. The pair must multiply to −15 and add to −2. The pairs are 1 and −15, −1 and 15, 3 and −5, −3 and 5. Only 3 and −5 add to −2. So x² − 2x − 15 = (x + 3)(x − 5).

Why it works: expanding (x + p)(x + q) gives x² + (p + q)x + pq, so the middle number is always the sum and the last number the product.

Try three

Tap a choice, or have a go and then tap to see the answer.

  1. 1.Factor: x² + 7x + 12

  2. 2.Expand: (x + 3)²

    Show the answer

    x² + 6x + 9. (x + 3)(x + 3) = x² + 3x + 3x + 9, and the two middle terms add to 6x.

  3. 3.Solve: x² − 2x − 15 = 0

    Show the answer

    x = 5 or x = −3. Factor to (x + 3)(x − 5) = 0. A product is zero only when one bracket is zero.

How Sparkpip fits in

Pip, Sparkpip's tutor, works through problems like these with your teen one small step at a time, using methods like the one above.

Start freeSee how it works

Your curriculum

Sparkpip is built on the grade 10 math curriculum for your province or state. The official pages:

Also: Grade 9 math · Grade 11 math · Grade 10 science · Grade 10 English