Daily Practice · Higher Plus
October 1997 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 1997, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 1997 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1997On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 2nd October 1997Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
- 3rd October 1997A quadratic sequence starts 9, 18, 33, 54. Work out the second difference, and the coefficient of n^2.
- 4th October 1997y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 5th October 1997In a vector proof you find that vector PQ = 4a - 4b and vector RS = 8a - 8b. What does this show about PQ and RS?
- 6th October 1997A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 7th October 1997A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 8th October 1997A rectangle is 27 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th October 1997Solve x^2 - 8x + 12 < 0.
- 10th October 1997y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 25.
- 11th October 1997A cuboid measures 6 cm by 5 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th October 1997A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th October 1997On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 14th October 1997Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 15th October 1997Write x^2 - 12x + 7 in the form (x + a)^2 + b.
- 16th October 1997A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 17th October 1997A cuboid measures 6 cm by 13 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th October 1997A bag holds 7 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th October 1997A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 20th October 1997A block has mass 380 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st October 1997Work out the coordinates of the turning point of y = x^2 - 16x + 5.
- 22nd October 1997y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 23rd October 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.
- 24th October 1997A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 25th October 1997On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 26th October 1997x = 171 and y = 28, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th October 1997Simplify (x^2 - 9x + 14)/(x - 7).
- 28th October 1997y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 29th October 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.
- 30th October 1997The probability of winning a game is 1/8. A player expects 15 wins. How many games did they play?
- 31st October 1997A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?