Daily Practice · Higher Plus
November 1997 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 1997, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 1997 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1997A car covers 100 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd November 1997In an algebraic proof, how would you write an odd number in terms of an integer n?
- 3rd November 1997y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 81.
- 4th November 1997In a vector proof you find that vector PQ = 6a - 5b and vector RS = 12a - 10b. What does this show about PQ and RS?
- 5th November 1997A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 6th November 1997On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 7th November 1997Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 8th November 1997Make x the subject of 8x + 6 = y(x + 6).
- 9th November 1997A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
- 10th November 1997A cuboid measures 10 cm by 8 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th November 1997A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th November 1997A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 13th November 1997Simplify sqrt(20) + sqrt(180), giving your answer in the form a sqrt(b).
- 14th November 1997Write 7/(x + 3) + 4/(x + 2) as a single fraction.
- 15th November 1997y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 16th November 1997A cuboid measures 12 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th November 1997A bag holds 4 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th November 1997On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th November 1997A rectangle is 28 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th November 1997Solve 6x^2 - x - 2 = 0.
- 21st November 1997y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 22nd November 1997The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 23rd November 1997A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.
- 24th November 1997A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 25th November 1997Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 26th November 1997f(x) = 4x + 12. Work out the inverse function f^-1(x).
- 27th November 1997y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 64.
- 28th November 1997In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 29th November 1997The probability of winning a game is 3/4. A player expects 66 wins. How many games did they play?
- 30th November 1997On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?