Equations and Inequalities: math test solutions, Grade 6 – download the PDF

1 Solve the equations / 4 pts

1. \(x = 40 - 13 = 27\) (1 pt)
2. \(y = 72 \div 9 = 8\) (1 pt)
3. \(m = 3.5 + 6.5 = 10\) (1 pt)
4. \(k = 8 \times 7 = 56\) (1 pt)

2 Is it a solution? / 3 pts

1. \(4 \times 5 = 20\): yes. (1 pt)
2. \(11 + 7 = 18 \neq 17\): no. (1 pt)
3. \(24 \div 6 = 4\): yes. (1 pt)

3 Equations from stories / 4 pts

1. Let \(m\) be the muffins sold later: \(36 + m = 91\) (1 pt). So \(m = 55\) (1 pt).
2. Let \(p\) be each share: \(4p = 52\) (1 pt). So \(p = 13\): each friend pays $13 (1 pt).

4 Inequalities / 4 pts

1. \(y < 12\) (1 pt)
2. \(w \leq 9\) (1 pt)
3. Closed circle at 9 and a ray going left (1 pt):
4. 7 and 9 are solutions; 10 is not (1 pt).

5 The museum / 3 pts

1. \(78 + v \leq 120\) (1 pt)
2. \(v \leq 42\) (1 pt)
3. No, because \(45 > 42\): the total would be 123, above the limit (1 pt).

6 The flower bed / 2 pts

\(9w = 63\) (1 pt). So \(w = 7\) ft, about 2.1 m (1 pt).