Daily Practice · Higher Plus
February 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 1998 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1998y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 2nd February 1998In a vector proof you find that vector PQ = 5a - b and vector RS = 10a - 2b. What does this show about PQ and RS?
- 3rd February 1998A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 4th February 1998A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 5th February 1998Simplify sqrt(45) + sqrt(45), giving your answer in the form a sqrt(b).
- 6th February 1998Simplify (x^2 - 7x - 8)/(x - 8).
- 7th February 1998y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 25.
- 8th February 1998A cuboid measures 4 cm by 12 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th February 1998A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th February 1998On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 11th February 1998A rectangle is 12 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th February 1998In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 13th February 1998A train slows steadily from 36 m/s to rest in 4 seconds. Work out its deceleration.
- 14th February 1998A cuboid measures 9 cm by 7 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th February 1998A bag holds 7 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th February 1998A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 17th February 1998Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).
- 18th February 1998Make x the subject of 4x + 8 = y(x + 8).
- 19th February 1998y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 20th February 1998The 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.
- 21st February 1998A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 22nd February 1998On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd February 1998A block has mass 230 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th February 1998Write 6/(x + 2) + 7/(x - 2) as a single fraction.
- 25th February 1998y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 26th February 1998In 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.
- 27th February 1998The probability of winning a game is 3/8. A player expects 9 wins. How many games did they play?
- 28th February 1998A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?