Daily Practice · Higher Plus
July 2000 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2000 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2000
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2000Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 2nd July 2000y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 3rd July 2000A cuboid measures 11 cm by 13 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th July 2000A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th July 2000On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 6th July 2000Simplify sqrt(8) + sqrt(18), giving your answer in the form a sqrt(b).
- 7th July 2000f(x) = 2x - 7 and g(x) = 4x + 8. Work out fg(-1).
- 8th July 2000y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 9th July 2000The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 10th July 2000A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 11th July 2000A 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?
- 12th July 2000A rectangle is 8 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th July 2000The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 14th July 2000y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 9.
- 15th July 2000In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 16th July 2000The probability of winning a game is 1/5. A player expects 11 wins. How many games did they play?
- 17th July 2000On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th July 2000Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 19th July 2000A quadratic sequence starts 11, 28, 53, 86. Work out the second difference, and the coefficient of n^2.
- 20th July 2000A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 21st July 2000In a vector proof you find that vector PQ = a + 3b and vector RS = 3a + 9b. What does this show about PQ and RS?
- 22nd July 2000A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 23rd July 2000A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 24th July 2000A block has mass 450 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.
- 25th July 2000Solve x^2 - 5x + 4 > 0.
- 26th July 2000y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 27th July 2000A cuboid measures 12 cm by 14 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th July 2000A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th July 2000On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th July 2000x = 114 and y = 49, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st July 2000Write x^2 - 14x - 11 in the form (x + a)^2 + b.