Daily Practice · Higher Plus
July 1997 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 1997, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 1997 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1997In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 2nd July 1997The probability of winning a game is 1/4. A player expects 15 wins. How many games did they play?
- 3rd July 1997A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 4th July 1997Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 5th July 1997Write x^2 + 6x - 5 in the form (x + a)^2 + b.
- 6th July 1997y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 49.
- 7th July 1997In a vector proof you find that vector PQ = 3a + 2b and vector RS = 6a + 4b. What does this show about PQ and RS?
- 8th July 1997A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 9th July 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?
- 10th July 1997Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
- 11th July 1997Work out the coordinates of the turning point of y = x^2 - 8x + 6.
- 12th July 1997A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 13th July 1997A cuboid measures 13 cm by 8 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th July 1997A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th July 1997A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 16th July 1997A rectangle is 5 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th July 1997Simplify (x^2 + 5x - 6)/(x - 1).
- 18th July 1997y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 19th July 1997A cuboid measures 8 cm by 5 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th July 1997A bag holds 6 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st July 1997On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd July 1997Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 23rd July 1997In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 24th July 1997y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 25th July 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.
- 26th July 1997A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 27th July 1997A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 28th July 1997A block has mass 240 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th July 1997Make x the subject of 2x + 7 = y(x + 7).
- 30th July 1997y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 25.
- 31st July 1997In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.