Daily Practice · Higher Plus
September 1997 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 1997, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 1997 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1997A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
- 2nd September 1997Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 3rd September 1997Work out the nth term of the quadratic sequence 3, 8, 17, 30, ...
- 4th September 1997y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 5th September 1997In a vector proof you find that vector PQ = a - 2b and vector RS = 4a - 8b. What does this show about PQ and RS?
- 6th September 1997A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 7th September 1997On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th September 1997A block has mass 900 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th September 1997The point (-4, 4) lies on y = f(x). Write down its image on y = f(x) + 1.
- 10th September 1997y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 11th September 1997A cuboid measures 6 cm by 6 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th September 1997A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th September 1997A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 14th September 1997x = 69 and y = 42, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th September 1997Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 16th September 1997y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 81.
- 17th September 1997A cuboid measures 6 cm by 13 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th September 1997A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th September 1997On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th September 1997A car covers 640 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st September 1997f(x) = 2x - 7 and g(x) = 2x - 7. Work out fg(6).
- 22nd September 1997A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd September 1997The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 24th September 1997A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 25th September 1997A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 26th September 1997Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 27th September 1997The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 28th September 1997y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 29th September 1997In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 30th September 1997The probability of winning a game is 1/5. A player expects 26 wins. How many games did they play?